Sample QuestionsProbability questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
What is the total number of sample spaces when a die is thrown $2$ times?
Answer: D.
View full solution →Choose the correct answer. In a non$-$leap year, the probability of having $53$ tuesdays or $53$ wednesdays is:
- ✓
$\frac{1}{7}$
- B
$\frac{2}{7}$
- C
$\frac{3}{7}$
- D
Answer: A.
View full solution →If $4-$digit numbers greater than $5000$ are randomly formed from the digits $0, 1, 3, 5$ and $7,$ then the probability of forming a number divisible by $5$ when the digits are repeated is:
- A
$\frac{1}{5}$
- ✓
$\frac{2}{5}$
- C
$\frac{3}{5}$
- D
$\frac{4}{5}$
Answer: B.
View full solution →Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals:
- A
$\frac{1}{2}$
- ✓
$\frac{7}{15}$
- C
$\frac{2}{15}$
- D
$\frac{1}{3}$
Answer: B.
View full solution →The equation $y^2+ 4x + 4y + k = 0$ represents a parabola whose latus rectum is:
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The probability of drawing either an ace or a king from a pack of cards in a single draw is $\frac{2}{13}.$
Reason: For two events $A$ and $B$ which are not mutually exclusive,
$\text{P}(\text{A}\cup\text{B})=\text{P}(\text{A})+\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B}).$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- ✓
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Consider the experiment of rolling a die. Then, sample space is $S = \{1, 2, 3, 4, 5, 6\}.$
Assertion: The event $EF : “$the number appears on the die is a multiple of $7”,$ is an impossible event.
Reason: The event $F : “$the number turns up is odd or even$”,$ is a sure event.
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- ✓
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A coin is tossed and then a die is rolled only in case a head is shown on the coin. The sample space for the experiment is $S = (H_1, H_2, H_3, H_4, H_5, H_6, T).$
Reason: $2$ boys and $2$ girls are in room $X,$ and $1$ boy and $3$ girls are in room $Y.$ Then, the sample space for the experiment in which a room is selected and then a person, is $S = \{XB_1, XB_2, XG_1, XG_2, YB_3, YG_3, YG_4, YG_5\}$ where $B_i,$ denote the boys and $G_j,$ denote the girls.
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- ✓
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A coin is tossed. If it shows head, we draw a ball from a bag consisting of $3$ brown and $4$ red balls; if it shows tail we throw a die, then the sample space of this experiment is $S = \{HB_1, HB_2, HB_3, HR_1, HR_2, HR_3, HR_4, T1, T2, T3, T4, T5, T6\}.$
Reason: Consider the experiment in which a coin is tossed repeatedly until a head comes up, then the sample space is $S = \{H, TH, TTH, TTTH,........ \}.$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- ✓
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Consider the experiment of rolling a die. Then, sample space is $S = \{1, 2, 3, 4, 5, 6\}.$
Assertion: If sample space of an experiment is $S = \{1, 2, 3, 4, 5, 6\}$ and the events $A$ and $B$ are defined as
$A :$ “a number less than or equal to $3$ appears”
$B :$ “ anumber greater than or equal to $3$ appears”,
then $A$ and $B$ are exhaustive events.
Reason: Events are exhaustive if atleast one of them necessarily occur whenever the experiment is performed.
- ✓
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
Answer: A.
View full solution →State whether the statements are True or False.
The probability of an occurrence of event A is 0.7 and that of the occurrence of event B is .3 and the probability of occurrence of both is 0.4
State whether the statements are True or False.
The sum of probabilities of two students getting distinction in their final examinations is 1.2
State whether the statements are True or False.
The probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11
State whether the statements are True or False.
The probability of intersection of two events A and B is always less than or equal to those favourable to the event A.
State whether the statements are True or False.
The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.
If 4-digit numbers greater than 5000 are randomly formed from the digits 0, 1, 3, 5, and 7. What is the probability of forming a number divisible by 5 when the repetition of digits is not allowed?
If $4-$digit numbers greater than 5000 are randomly formed from the digits $0, 1, 3, 5,$ and $7$ what is the probability of forming a number divisible by $5$ when the digits are repeated?
View full solution →In a certain lottery 10,000 tickets are sold and, ten equal prizes are awarded. What is the probability of not getting a prize if you buy 10 tickets?
In a certain lottery 10,000 tickets are sold and, ten equal prizes are awarded. What is the probability of not getting a prize if you buy two tickets?
In a certain lottery 10,000 tickets are sold and, ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket?
Three letters are written to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
4 cards are drawn from a well shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that at least one will be green?
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that all will be blue?
There are four men and, six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?
From the employees of a company, 5 persons are selected to represents them in the managing committee of the company particulars of five persons are as follows:
| S.No. | Name | Sex | Age in years |
| 1 | Harish | M | 30 |
| 2 | Rohan | M | 33 |
| 3 | Sheetal | F | 46 |
| 4 | Alice | F | 28 |
| 5 | Salim | M | 41 |
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
Out of $100$ students, two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students, what is the probability that,
- you both enter the same section?
- you both enter the different sections?
View full solution →The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e. from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
A fair coin is tossed four times, and a person win Re $1$ for each head, and lose Rs. $1.50$ for each tail that turns up. Form the sample space, calculate how many different amounts of money he can have after four tosses and the probability of having each of these amounts.
View full solution →A letter is chosen at random from the word ASSASSINATION find the probability that letter is a consonant.
Fill in the blanks.
If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and $\text{P}(\text{A}\cap\text{B})=0.1,$ then the value of $\text{P}(\text{A}\cap\bar{\text{B}})$ is ____________.
View full solution →Fill in the blanks.
Let S = {1, 2, 3, 4, 5, 6} and E = {1, 3, 5}, then $\bar{\text{E}}$ is __________.
View full solution →Fill in the blanks.
If $e_1, e_2, e_3, e_4 $ are the four elementary outcomes in a sample space and $P(e_1) = 0.1, P(e_2) = 0.5, P (e_3) = 0.1,$ then the probability of $e_4 $ is ___________.
View full solution →Fill in the blanks.
The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is __________.
Fill in the blanks.
The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is __________.
$A$ and $B$ are two events such that $P(A) = 0.54, P(B) = 0.69$ and $P(A \cap B) = 0.35$. Find
- $P(A \cup B)$
- $P(A'\cap B')$
- $P(A\cap B')$
- $P( B\cap A')$
View full solution →If $\frac2{11}$ is the probability of an event A, what is the probability of the event 'not A'.
View full solution →In a lottery, a person chosen, six different natural numbers at random from 1 to 20 and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?
[Hint order of the numbers is not important.]
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
A: the sum is greater than 8, B: 2 occurs on either die.
C: the sum is at least 7 and a multiple of 3
which pairs of these events are mutually exclusive?
A die is thrown. Describe the following events:
- $A:$ a number less than $7$
- $B:$ a number greater than $7$
- $C:$ a multiple of $3$
- $D:$ a number less than $4$
- $E:$ an even number greater than $4$
- $F:$ a number not less than $3$
Also find $\ce{{A\cup B}, {A\cap B}, {B\cup C}, {E\cap F}, {D\cap E}, A –C, D–E, {E\cap F'}, F'.}$ View full solution →