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Mathematics [1 Mark Question Answer]

Probability · ICSE STD 10 (ICSE - English Medium). 49 questions.

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[1 Mark Question Answer]

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49 questions · timed · auto-graded

Question 11 Mark
In a match between A and B: the probability of losing the match is 0.49 for B. What is the probability of winning of A?
Answer
Probability of winning of B+Probability of losing of B=1 Probability of losing of B = Probability of winning of A Therefore, Probability of winning of A=0.49
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Question 21 Mark
In a match between A and B: the probability of winning of A is 0.83. What is the probability of winning of B?
Answer
Probability of winning of A+ Probability of losing of A=1 Probability of losing of A=Probability of winning of B Therfore, Probability of winning of A+ Probability of winning of B=1 0.83+Probability of winning of B =1-1.0.83=0.17
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Question 31 Mark
From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is: a card with number between 2 and 9
Answer
Total number of possible outcomes=52
n(s)=52
Number between 2 and 9 = {3,4,5,6,7,8}
Event of drawing card with number between 2 and 9=E= {6H cards,6D cards,6Ss cards,6c cards}
n(E)=24
Probability of drawing a card with number between 2 and 9= $\frac{n(E)}{n(S)}=\frac{24}{52}=\frac{6}{13}$
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Question 41 Mark
From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is a card with number less than 8
Answer
Total number of possible outcomes=52
n(s) = 52
Number less than 8={2,3,4,5,6,7}
Event of drawing a card with number less than 8 = E = [ 6H cards , 6D cards ,6s cards ,6c cards]
n(E) = 24
Probability of drawing a card with number less than 8 =$\frac{n(E)}{n(s)}=\frac{24}{52}=\frac{6}{13}$
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Question 51 Mark
From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is: a card with number 5 or 6
Answer
Total number of possible outcomes=52
n(s)=52
Event of drawing a card with number 5 or 6 =E={5H,5D,5S,5C,6H,6D,6S,6C}
n(E)=8
Probability of drawing a card with number 5 or 6
$\frac{n(E)}{n(S)}=\frac{8}{52}=\frac{2}{13}$
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Question 61 Mark
From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is: a queen of black card.
Answer
Event of drawing a queen of black colour={Q (spande), Q(club)=E}
n(E)=2
Probability of drawing a queen of black colour=
$\frac{n(E)}{n(s)}=\frac{2}{52}=\frac{1}{26}$
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Question 71 Mark
From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is: not a face card
Answer
Total number of possible outcomes=52
n(s)=52
Probability of not drawing a face card =1-Probability of drawing a face card probability of not drawing face card =$1-\frac{3}{13}=\frac{13-3}{13}=\frac{10}{13}$
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Question 81 Mark
A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears: a perfect square number
Answer
Total number of posibble outcomes $=100$
Number which are perfeect squares=
$
1,4,9,16,25,36,49,64,81,100
$
Number of favorable outcome $=10$
$
p(a \text { perfect square })=\frac{10}{100}=\frac{1}{10}
$
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Question 91 Mark
A box contains 150 bulbs out of which 15 are defective. It is not possible to just look at a bulb and tell whether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is: a defective one
Answer
Total number of possible outcomes $=150$
Number of bulbs which are defective $=15$
$P \left(\right.$ taking out a defective bulb) $=\frac{15}{150}=\frac{1}{10}$
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Question 101 Mark
Seven cards:- the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random. What is the probability that the card drawn is the eight or the king?
Answer
Total number of possible outcomes=7
Number of favorable outcomes for the card is 8 or the king =2
p(card is 8 or the king) = 2/7
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Question 111 Mark
A bag contains a certain number of red balls. A ball is drawn. Find the probability that the ball drawn is: red
Answer
Number of favorable outcomes for red balls = number of red balls p(red ball)
Image
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Question 121 Mark
A bag contains a certain number of red balls. A ball is drawn. Find the probability that the ball drawn is : black
Answer
Total possible outcomes= number of red balls. Number of favorable outcomes for black balls =0 p(black ball )=0
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Question 141 Mark
Which of the following cannot be the probability of an event? -2.4
Answer
We know that probability of an event $E$ is $0 \leq p(E) \leq 1$
Since - 2.4 < 0
Therefore, -2.4 cannot be a Probability of an event.
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Question 151 Mark
Which of the following cannot be the probability of an event? 37%
Answer
We know that probabilty of an event $E$ is $0 \leq P(E) \leq 1$
Since $0 \leq 37 \%=\left(\frac{37}{100}\right) \leq 1$
therefore, $37 \%$ can be a probability of an event.
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Question 161 Mark
Which of the following cannot be the probability of an event? 0.82
Answer
We know that probabilty of an event $E$ is $0 \leq P(E) \leq 1$ Since $0 \leq 0.82 \leq 1$
Therefore, 0.82 can be a probability of an event.
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Question 171 Mark
Which of the following cannot be the probability of an event? 3/7
Answer
We know that probabilty of an event E is $0 \leq P(E) \leq 1$
Since $0 \leq \frac{3}{7} \leq 1$
Therefore, $\frac{3}{7}$ can be a probability of an event.
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Question 181 Mark
Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is: less than or equal to 12
Answer
The number of possible outcomes =$6 \times 6=36$
All the outcomes are favourable to the event E=sum of two number $\leq 12$ :
Hence, p(E)=$\frac{n(E)}{n(S)}$ = $\frac{36}{36}$ = 1
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Question 191 Mark
Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is : 13.
Answer
The number of possible outcomes =$6 \times 6=36$
There is no outcome favourable to the event E=the sum of two number is 13 .
n(E)=0
Hence, $p(E)=\frac{n(E)}{n(s)}=\frac{0}{36}$
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Question 201 Mark
A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is: a red and a king
Answer
Number of possible outcomes when card is drawn from pack of 52 cards=52
n(E) = 2
event of drawing a red and a king=$\frac{n(E)}{n(s)}=\frac{2}{52}=\frac{1}{26}$
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Question 211 Mark
If A and B are two complementary events then what is the relation between P(A) and P(B)?
Answer
Two complementary events, taken together, include all the outcomes for an experiment and the sum of the probabilities of all outcomes is 1.
P(A) + P(B) = 1
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Question 221 Mark
From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will be a face card of red colour.
Answer
There are 26 red cards in a deck , and 6 of these cards are face cards (2 kings, 2 queens, 2 jacks).
p(E)=6
probability of drawing a red face card =
$\frac{ p ( E )}{ p ( s )}=\frac{6}{52}=\frac{3}{26}$
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Question 231 Mark
A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out: a black ball
Answer
E= event of drawing a black ball = number of black in this bag =6
probability of drawing a black ball =
$P(s)=\frac{n(E)}{n(S)}=\frac{6}{6}=1$
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Question 241 Mark
following are cannot be the probability of an event? -3.2
Answer
$-3.2$
$-3.2 \leq 0 \leq 1$
Hence, it cannot be the probablity of an event.
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Question 251 Mark
following are cannot be the probability of an event? -0.6
Answer
$-0.6$
$-0.6 \leq 0 \leq 1$
Hence, it cannot be the probability of an event
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Question 261 Mark
Which of the following cannot be the probability of an event? 43%
Answer
$43 \%=\frac{43}{100}=0.43$
$0 \leq 0.43 \leq 1$
Hence, it can be the probability of an event.
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Question 271 Mark
Whivh of the following are cannot be the probability of an event? : 2.7
Answer
2.7
$\because \leq 1 \leq 2.7$
Hence, it cannot be the probability of an event.
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Question 281 Mark
Which of following cannot be the probability of an event ?
$\frac{3}{5}$
Answer
The probability of an event lies betweet '0' and '1' i.e 0 ≤ P(E) ≤1.
$\frac{3}{5}=0.6$
$\because 0 \leq 0.6 \leq 1$
Hence, it can be the probability of an event. .
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Question 291 Mark
A die is thrown once. Find the probability of getting: a number between 3 and 8
Answer
E= the possible even number between 3 and 8 ={4,5,6}
n(E)=3
probability of getting an even number between 3 and
$8=p(s)=\frac{n(E)}{n(s)}=\frac{3}{6}=\frac{1}{2}$
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Question 301 Mark
In a match between A and B:   the probability of losing the match is 0.49 for B. What is the probability of winning of A?   
Answer
Probability of winning of B+Probability of losing of B=1 Probability of losing of B = Probability of winning of A Therefore,
Probability of winning of A=0.49
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Question 311 Mark
A box contains 150 bulbs out of which 15 are defective. It is not possible to just look at a bulb and tell whether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is:   a defective one 
Answer
Total number of possible outcomes $=150$
Number of bulbs which are defective $=15$
$P \left(\right.$ taking out a defective bulb) $=\frac{15}{150}=\frac{1}{10}$
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Question 321 Mark
Seven cards:- the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random.
What is the probability that the card drawn is the eight or the king? 
Answer
Total number of possible outcomes=7
Number of favorable outcomes for the card is 8 or the king =2
p(card is 8 or the king)=2/7
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Question 331 Mark
The probability that two boys do not have the same birthday is 0.897. What is the probability that the two boys have the same birthday? 
Answer
P(do not have the same birthday)+P(have same birthday) = 1
0.897 + P(have same birthday) = 1
P(have same birthday) = 1 – 0.897
P(have same birthday) = 0.103
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Question 341 Mark
A bag contains a certain number of red balls. A ball is drawn. Find the probability that the ball drawn is:
red
Answer
Number of favorable outcomes for red balls = number of red balls p(red ball)
Image
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Question 351 Mark
A bag contains a certain number of red balls. A ball is drawn. Find the probability that the ball drawn is:
black
Answer
Total possible outcomes= number of red balls.
Number of favorable outcomes for black balls =0
p(black ball )=0 
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Question 361 Mark
If P(E) = 0.59; find P(not E) 
Answer
P(E) + P(not E) = 1
0.59 + P(not E) = 1
P(not E) = 1 – 0.59 = 0.41
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Question 371 Mark
Which of the following cannot be the probability of an event?
-2.4
Answer
We know that probability of an event $E$ is $0 \leq p(E) \leq 1$
Since-2.4<0
Therefore, -2.4 cannot be a Probability of an event.
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Question 381 Mark
Which of the following cannot be the probability of an event?
37%
Answer
We know that probabilty of an event $E$ is $0 \leq P(E) \leq 1$
Since $0 \leq 37 \%=\left(\frac{37}{100}\right) \leq 1$
therefore, $37 \%$ can be a probability of an event.
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Question 391 Mark
Which of the following cannot be the probability of an event?
0.82
Answer
We know that probabilty of an event $E$ is $0 \leq P(E) \leq 1$ Since $0 \leq 0.82 \leq 1$
Therefore, 0.82 can be a probability of an event.
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Question 401 Mark
Which of the following cannot be the probability of an event?
3/7
Answer
We know that probabilty of an event E is $0 \leq P(E) \leq 1$
Since $0 \leq \frac{3}{7} \leq 1$
Therefore, $\frac{3}{7}$ can be a probability of an event.
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Question 411 Mark
 If A and B are two complementary events then what is the relation between P(A) and P(B)?
Answer
Two complementary events, taken together, include all the outcomes for an experiment and the sum of the probabilities of all outcomes is 1.
P(A) + P(B) = 1
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Question 421 Mark
In a single throw of a die, find the probability of getting a number:
not greater than 4.
Answer
E=event of getting number not greater than
4={1,2,3,4}
n(E)=4
probability of a number not grearer than 4
$\frac{ n ( E )}{ n ( s )}=\frac{4}{6}=\frac{2}{3}$
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Question 431 Mark
A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is:
not a red ball.
Answer
There are 3+5=8 balls which are not red
Favourable number of events= P(A)=8
Hence, P (not getting a red ball) =$\frac{P(A)}{P(n)}=\frac{8}{10}=\frac{4}{5}$
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Question 441 Mark
A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out:   a black ball
Answer
E= event of drawing a black ball = number of black in this bag =6
probability of drawing a black ball =
$P(s)=\frac{n(E)}{n(S)}=\frac{6}{6}=1$
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Question 451 Mark
Which of the following cannot be the probability of an event?
0.35
Answer
0.35
$0 \leq 0.35 \leq 1$
Hence, it can be the probability of an event.
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Question 461 Mark
following are cannot be the probability of an event?
-3.2
Answer
$-3.2$
$-3.2 \leq 0 \leq 1$
Hence, it cannot be the probablity of an event.
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Question 471 Mark
following are cannot be the probability of an event?
-0.6
Answer
$-0.6$
$-0.6 \leq 0 \leq 1$
Hence, it cannot be the probability of an event
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Question 481 Mark
Which of the following cannot be the probability of an event?
43%
Answer
$43 \%=\frac{43}{100}=0.43$
$0 \leq 0.43 \leq 1$
Hence, it can be the probability of an event.
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Question 491 Mark
Which of the following are cannot be the probability of an event?
2.7
Answer
2.7
$\because \leq 1 \leq 2.7$
Hence, it cannot be the probability of an event.
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[1 Mark Question Answer] - Mathematics STD 10 Questions - Vidyadip