MCQ 11 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If a die is thrown, the probability of getting a number less than $3$ and greater than $2$ is zero.
Reason : Probability of an impossible event is zero.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
View full question & answer→MCQ 21 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : When two coins are tossed simultaneously then the probability of getting no tail is $\frac{1}{4}$
Reason : The probability of getting a head $($i.e., no tail$)$ in one toss of a coin is $\frac{1}{2}$
- A
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- ✓
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
If Assertion is true but Reason is false.
- D
If Assertion is false but Reason is true.
AnswerCorrect option: B. If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
Probability of both head
$=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$
View full question & answer→MCQ 31 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : The probability of getting a prime number, When a die is throw $n$ once is $\frac{2}{3}$
Reason : Prime numbers on a die are $2, 3, 5.$
- A
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
If Assertion is true but Reason is false.
- ✓
If Assertion is false but Reason is true.
AnswerCorrect option: D. If Assertion is false but Reason is true.
When a die is thrown once, total possible outcomes $= 6$
and prime numbers in it are $(2, 3, 5)$
Total favourable outcomes $= 3$
Probability of getting a prime $=\frac{3}{6}=\frac{1}{2}$
View full question & answer→MCQ 41 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : An event is very unlikely to happen.Its probability is $0.0001.$
Reason : If $P(A)$ denote the probability of an event $A,$ then $0\leq\text{P(A)}\leq1$
- A
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- ✓
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
If Assertion is true but Reason is false.
- D
If Assertion is false but Reason is true.
AnswerCorrect option: B. If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
The probability of an event to be unlikely if the probability is near to $‘0’$.
As $0.0001$ is near to $0,$ the occuring of event is unlikely.
Now, we know probability of an event lies in between $0$ and $1$ because total possibilities will be always greater than equal to favourable outcomes.
View full question & answer→MCQ 51 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : When two coins are tossed simultaneously then the probability of getting no tail is $\frac{1}{4}$
Reason : The probability of getting a head $($ie., no $+7$ tail$)$ in one toss of a coin is $\frac{1}{2}$
- ✓
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
Assertion is true but Reason is false.
- D
Assertion is false but Reason is true.
AnswerCorrect option: A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
Probability of getting no tail when two coins tossed simultaneously
i.e., both are head. Probability ili of both head $=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$
View full question & answer→MCQ 61 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If $\text{P(A)} =0.25, $
$\text{P(B)}=0.50$ and $\text{P(A}\cap\text{B})=0.14,$ then the probability that neither $\text{A}$ or $\text{B}$ occurs is $0.39.$
Reason : $\overline{\text{A}\cup\text{B}}=\overline{\text{A}}\cup\overline{\text{B}}$
- A
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- ✓
Assertion is true but Reason is false.
- D
Assertion is false but Reason is true.
AnswerCorrect option: C. Assertion is true but Reason is false.
View full question & answer→MCQ 71 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : In a simultaneously throw a pair of dice.The probability of getting a double is $\frac{1}{6}$
Reason : Probability of an event may be negative.
- A
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- ✓
If Assertion is true but Reason is false.
- D
If Assertion is false but Reason is true.
AnswerCorrect option: C. If Assertion is true but Reason is false.
When two dice are tossed.
Total possible outcomes $= 36$
$n(S) = 36$
and total favourable outcomes (doublet)
$= \{(1, 1), (2; 2), (3, 3), (4, 4), (5, 5), (6, 6)\}$
$n( E) = 6$
$\therefore$ Probability $=\frac{6}{36}=\frac{1}{6}$ and
We know that, $ 0\leq\text{P(E)}\leq1$
View full question & answer→MCQ 81 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : Card numbered as $1, 2, 3$ bevees $15$ are put in a box and mixed throughly, one card is then drawn at random.The probability of drawing an even number is a
Reason : For any event $\text{E},$ we have $\text{O}\leq\text{P(E)}\leq1.$
- A
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
If Assertion is true but Reason is false.
- ✓
If Assertion is false but Reason is true.
AnswerCorrect option: D. If Assertion is false but Reason is true.
View full question & answer→MCQ 91 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Let $A$ and $B$ be two independent events.
Assertion : If $\text{P}\text{(A)}=0.3$ and $\text{P}(\text{A}\cup\overline{\text{B}}) =0.8,$ then $\text{P}(\text{B})$ is $\frac{2}{7}$
Reason : $\text{P}\overline{\text{E}}=1-\text{P}(\text{E}),$ where $\text{F}$ is any event.
- ✓
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
Assertion is true but Reason is false.
- D
Assertion is false but Reason is true.
AnswerCorrect option: A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
Probability of getting no tail when two coins tossed simultaneously
i.e., both are head.
Probability ili of both head $=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$
View full question & answer→MCQ 101 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$.Mark the correct choice as:
Assertion : An event is very unlikely to happen.Its probability is $0.0001$
Reason : If $P(A)$ denote the probability of an event $\text{A,}$ then $0\leq\text{P(A)}\leq1.$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
View full question & answer→MCQ 111 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If a die is thrown, the probability of getting a number less than $3$ and greater than $2$ is zero.
Reason : Probability of an impossible event is zero.
- ✓
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
If Assertion is true but Reason is false.
- D
If Assertion is false but Reason is true.
AnswerCorrect option: A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
Now, where dice is thrown the possible outcomes are $\{(1, 2, 3, 4, 5, 6)\}, $
Now, if you see the outcomes getting a number greater than $"2" $ and less than $"3"$ is impossible.
$\therefore$ Probability is zero
The probability of an impossible event
$= 0$
View full question & answer→MCQ 121 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If the probability of an event is $P,$ then probability of its complementary event will be $1 - P.$
Reason : When $\text{E}$ and $\overline{\text{E}}$ are complementary events, then $\text{P(E)}+\text{P}\overline{\text{E}}=1$
- ✓
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
If Assertion is true but Reason is false.
- D
If Assertion is false but Reason is true.
AnswerCorrect option: A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
$=$ Sum of probability of an event and its complementary event $= 1$
$\Rightarrow\text{P(E)}+\text{P}\bar{(\text{E})}=1$
$\Rightarrow\text{P}\bar{(\text{E})}=1-\text{P}(\overline{\text{E}})$
View full question & answer→MCQ 131 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If a box contains $5$ white $,2$ red and $4$ black marbles, then the probability of not drawing a white marble from the box is a $\frac{5}{11}$
Reason: $\text{P(E)}=1-\text{P(E)},$ where $\text{E}$ is any evnet.
- A
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
Assertion is true but Reason is false.
- ✓
Assertion is false but Reason is true.
AnswerCorrect option: D. Assertion is false but Reason is true.
Assertion $(A)$ is false but reason $(R)$ is true.
Assertion is not correct, but reason is correct.
$P($white marble$) =\frac{5}{5+2+4}=\frac{5}{11}$
$P($not white marble$) =1-\frac{5}{11}$
$=\frac{11-5}{11}=\frac{6}{11}$
View full question & answer→MCQ 141 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : The probability of winning a game is $0.4,$ then the probability of losing it, is $0.6.$
Reason : $P(E) + P($not $E) = 1.$
- ✓
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
If Assertion is true but Reason is false.
- D
If Assertion is false but Reason is true.
AnswerCorrect option: A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
We have, $P(E) =04$
where $E =$ event of winning
$P($Not $EZ) =1- P(E) $
$=1- 04 = 06$z
View full question & answer→MCQ 151 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If a box contains $5$ white $, 2$ red and $4$ black marbles, then the probability of not drawing a white marble from the box is $\frac{5}{11}$
Reason : $\text{P(E)} =1- \text{P}(\overline{\text{E}}),$ where $\text{E}$ is any event.
- A
If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- C
If Assertion is true but Reason is false.
- ✓
If Assertion is false but Reason is true.
AnswerCorrect option: D. If Assertion is false but Reason is true.
$P \ ($white marble$) =\frac{5}{5+2+4}=\frac{5}{11}$
$P \ ($not white marble$) =1-\frac{5}{11}$
$=\frac{11-5}{11}=\frac{6}{11}$
View full question & answer→MCQ 161 Mark
Statement A (Assertion) : A number is selected from the numbers 1 to 20 . The probability that it will be a prime is $\frac{2}{5}$.
Reason (R) : There exists 25 prime numbers from natural number 1 to 100 .
- A
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
(b):Clearly, Reason is true.
Now, total number of outcomes $=20$
Favourable outcomes are $\{2,3,5,7,11,13,17,19\}$ i.e., 8 in number.
$\therefore \quad$ Required probability $=\frac{8}{20}=\frac{2}{5}$
$\therefore \quad$ Assertion and Reason both are true but Reason is not the correct explanation of Assertion.
View full question & answer→MCQ 171 Mark
Statement A (Assertion) : Two dice are rolled simultaneously. Then the probability of getting prime number on both dice is $\frac{1}{4}$.
Statement R (Reason) : Sum of probabilities of all the elementary events of an experiment is zero.
- A
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
(c):Clearly, Reason is false.
Now, total number of possible outcomes, when two dice are rolled simultaneously $=6 \times 6=36$
Favourable outcomes are $\{(2,2),(2,3),(2,5),(3,2)$, $(3,3),(3,5),(5,2),(5,3),(5,5)\}$ i.e., 9 in number.
$\therefore \quad$ Required probability $=\frac{9}{36}=\frac{1}{4}$
$\therefore \quad$ Assertion is true.
View full question & answer→MCQ 181 Mark
Statement A (Assertion) : In a game, the entry fee is ₹ 10. The game consists of tossing of 3 coins. If one or two heads show, Amita win the game and gets entry fee. The probability, that she gets the entry fee is $\frac{3}{4}$.
Statement R (Reason): When three coins are tossed together, all the outcomes are {H H H, HHT, HTH, THH, HTT, THT, TTH and TTT }.
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
(a):Clearly, Reason is true.
Now, in case of tossing three coins, total number of possible outcomes $=8$
Favourable outcomes are { H H T, H T H, T H H, H T T, T H T, TTH} i.e., 6.
$\therefore \quad$ Required probability $=\frac{6}{8}=\frac{3}{4}$
So, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 191 Mark
Statement A (Assertion) : Seven face cards are removed from a deck of cards and the cards are well shuffled. Then the probability of drawing a face card is $\frac{5}{52}$.
Statement R (Reason) : King, Queen and Jack are known as face cards. So, there are 12 face cards in total.
- A
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion (A) is false but reason $(R)$ is true.
(d):Clearly, Reason is true.
Total number of possible outcomes $=52-7=45$
$\because \quad$ Remaining number of face cards $=12-7=5$
So, favourable number of outcomes $=5$
$\therefore \quad$ Required probability $=\frac{5}{45}=\frac{1}{9}$
$\therefore \quad$ Assertion is false.
View full question & answer→MCQ 201 Mark
Statement A (Assertion): In a single throw of a die. The probability of getting a number less than 7 is 1 .
Statement R (Reason) : The probability of a certain event is 1 .
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
(a):Clearly, Reason is true.
Now, in a single throw of a die, all the possible outcomes are $(1,2,3,4,5,6)$.
Since, all the numbers are less than 7 , then it is a sure event.
$\therefore \quad$ The probability of getting a number less than 7 is 1 . So, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 211 Mark
Statement A (Assertion): Cards numbered 5 to 102 are placed in a box. If a card is selected at random from the box, then the probability that the card selected has a number which is a perfect square, is $\frac{4}{49}$.
Statement R (Reason) : Probability of an event $E$ is a number such that $0 \leq P(E) \leq 1$.
- A
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
(b):Clearly, Reason is true.
Total number of cards $=102-5+1=98$
So, total number of possible outcomes $=98$
Let $E$ be the event of selecting a card with perfect square number on it.
So, favourable outcomes to $E$ are $\{9,16,25,36,49,64$, $81,100\}$ i.e., 8 $ \therefore \quad P(E)=\frac{8}{98}=\frac{4}{49} $
So, Assertion and Reason both are true but Reason is not the correct explanation of Assertion.
View full question & answer→MCQ 221 Mark
Statement A (Assertion): Three unbiased coins are tossed together, then the probability of getting exactly 1 head is $\frac{3}{8}$.
Statement R (Reason) : Favourable number of outcomes do not lie in the sample space of total number of outcomes.
- A
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
(c):$\because$ Favourable outcomes always lies in the sample space of total number of outcomes. So, Reason is false.
Total possible outcomes are $1 HHH , HHT , HTH , THH$, TTH, THT, HTT, TTT] i.e., 8 in number. Let $E$ be the event of getting exactly 1 head.
$\therefore \quad$ Outcomes favourable to $E$ are $[T T H, T H T, H T T]$ i.e., 3 in number. $ \therefore \quad P(E)=\frac{3}{8} $
$\therefore \quad$ Assertion is true.
View full question & answer→MCQ 231 Mark
Statement A (Assertion) : Two dice ar thrown simultaneously. There are 11 possible outcomes of their sum $\{(3,4,5,6,7,8,9,10,11$ $12,13)\}$ and each of them are equally likely.
Statement R (Reason) : Probability of ar event $E$ is defined as :
$P(E)=\frac{\text { Number of outcomes favourable to } E}{\text { Total number of possible outcomes }}$
- A
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion (A) is false but reason $(R)$ is true.
(d):Clearly, Reason is true.
Now, if two dice will be thrown simultaneously, then the possible outcomes of their sum will be $\{2,3,4,5,6$, $7,8,9,10,11,12\}$ and probability of each outcome is not equally likely.
$\therefore \quad$ Assertion is false.
View full question & answer→MCQ 241 Mark
Statement A (Assertion) : Two players Sania and Deepika play a tennis match. If the probability of Sania winning the match is 0.68 , then the probability of Deepika winning the match is 0.32 .
Statement R (Reason) : The sum of the probabilities of two complementary events is 1 .
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion (A) and reason ( $R$ ) are true and reason (R) is the correct explanation of assertion (A).
(a):Clearly, Reason is true.
Let $E$ be the event 'Sania win the match'.
So, probability of Sania winning the match $=P(E)=0.68$
$ \because \quad P(E)+P(\bar{E})=1 $
$\therefore \quad$ Probability of Deepika winning the match $=P(\bar{E})$
$ =1-0.68=0.32 $
So, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→