MULTIPLE CHOICE QUESTIONS CHAPTER – 13 13 PROBABILITY Q1. If
A
and B are independent events such that P A 0.4 , P B x and P A
(a) 4 5
Q2. If
A
(b)
0.1
and B are events such that P A
(a) independent
1 2
(c) , P B
7
Q3. It is given that probability that
A can
Q4. The probabilities of
(b) 1 15 A , B
B
solve a given problem is
solve the same problem is 2 3 . The probability that at least one of (a) 2 5
'
'
x
=?
1
4 , then A and B are:
(c) both ‘a’ and ‘b’
(b) mutually exclusive
0.5 , then
(d) None of these
1 6
and P A
12
B
A
3 5 and
(d) None of these
the probability that
B
can
and B can solve a problem is:
(c) 13 15
(d)
2 15
and C of solving a problem are 1 6 ,1 5 , 1 3 respectively. The probability
that the problem is solved is? (a) 4 9
Q5. If
A
(b) 5 9
and B are two events such that P A
(a) independent
(b) dependent
(c)
B
5 6
, P A
(d) None of these
13
B
1 3
and P B '
1 2
(c) mutually exclusive
, then
A
and B are:
(d) None of these
Q6. Two numbers are selected at random from integers 1 through 9. If the sum is even, the probability
that both numbers being odd is: (a)
1 6
(b) 2 3
(c) 4 9
(d)
5 8
Q7. Assume that in a family, each child is equally likely to be a boy or a girl. A family with three
children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is: (a)
1 2
(b)
1 3
(c) 2 3
(d) 4 7
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Q8. If one ball is drawn at random from each of three boxes containing 3 white and 1 black, 2 white and
2 black, 1 white and 3 black balls, then the probability that 2 white and 1 black balls will be drawn is: (a) 13 32
(b)
1 4
(c)
1 32
(d)
3 16
Q9. Three integers are chosen at random from first 20 integers. Probability that their product is even is:
(a)
(c) 17 19
(b) 3 29
2 19
(d)
4 19
Q10. An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at
random. The probability that they are of o f the same colour is: (a)
5 84
(b)
3 9
(c) 3 7
(d)
7 17
Q11. A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, the
probability of getting exactly one red ball is: (a) 45 196 Q12. Two persons
(b) 135 392 A
9 17
(d) 15 29
and B take turns in throwing a pair of dice. The first person to throw a total of 9
from both dice will be awarded the prize. If (a)
(c) 15 56
(b)
8 17
A throws
first, then the probability that
(c)
8 9
(d)
B wins
the same is:
19
Q13. From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the
number obtained on the card is divisible by 6 or 8 but not by 24 is: (a) 6 25
(b)
1 4
(c)
1 6
(d) 4 5
Q14. There are two bags I and II. Bag I contains 4 white and 3 red balls while Bag II contains 3 white
and 7 red balls. One ball is drawn at random from one of the bags and is found to be white. The probability that it was drawn from Bag I is: is: (a)
30 61
(b)
40 61
(c)
29 61
(d) None of these
Q15. In a bolt factory, machines A, B and C manufacture 60% , 25% and 15% respectively. Of the total
of their output 1% , 2% and 1% are defective bolts. A bolt is drawn at random from the total production and found to be defective. The probability that the defective bolt is manufactured by machine B is: (a) 12 25
(b) 3 25
(c) 10 25
(d) None of these
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Q16. A man speaks 75% times the truth. He throws a die and reports that it is a six. The probability that it
is actual 6 is: (a)
1 8
(b)
3 8
(c)
1 2
(d)
5 8
Q17. A box contains 4 red, 6 blue and 5 white balls. A man draws one ball at random. If he draws a red
ball, he gets Rs 6, 6 , if he draws a blue ball, he gets Rs. 3 , and he pays Rs. 3 if he gets a white ball. The expected value of his gain is: (a) 4 5
(b) 7 5
(c) 9 5
(d) None of these
Q18. A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of
rounds, he must fire in order to have mor e than 50% chance of hitting it at least twice is: (a) 11
(b) 9
(c) 7
Q19. A fair coin is tossed 99 times. If
when
X is
(d) 5
the number of times heads occur, then
r is maximum
P X
r is:
(a) 49, 50
(b) 50, 51
(c) 51, 52
(d) None of these
Q20. A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to
that of getting nine heads, the probability of getting two heads is: (a) 15 28
(b)
(c) 15 213
2 15
(d) None of these
Q21. The least number of times a fair coin must be tossed so that the probablilty of getting at least one
head is at least 0.8 is, (a) 7
(b) 6
(c) 5
(d) 3
Q22. A fair dice is tossed eight times. The probab ility that a third six is observed in the eighth throw is: C 2 5
7
(a)
5
6
7
C 2 5
7
(b)
5
8
6
C 2 5
7
(c)
5
6
(d) None of these
6
Q23. The mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of
getting exactly six successes is: 10
1 3 (a) C 6 4 4 16
6
6
10
1 3 (b) C 6 (c) 4 4 16
6
1 3 C 6 20 4
12
6
1 3 (d) C 6 4 4
6
12
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Q24. Probability of guessing correctly at least 8 o ut of 10 answers on a true -false type examination is:
(a) 7 64
(b)
7 128
(c) 45 1024
(d) 7 41
Q25. A fair coin is tossed 6 times. The probability of getting at least 3 heads is:
(a)
11 16
(b)
21 32
(c)
1 18
(d)
3 64
Q26. A die is thrown 5 times. If getting an odd number is a success, the probability of getting at least 4
successes is: (a)
4 5
(b)
7 16
(c)
3 16
(d)
3 20
Q27. A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, the probability of
getting at most 6 successes is: 7
5 (a) 6
7
1 (b) 6
1 (c) 1 6
7
(d) None of these
Q28. The probability that a man can hit a target is 3 4 . He tries five times. The probability that he will
hit the target at least three times is: (a)
459 512
(b)
291 364
(c)
371
(d) None of these
464
Q29. A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn
one by one with replacement at most one is defective is: 5
9 (a) 10
(b)
1 9
4
2 10
(c)
1 9
2 10
5
5
9 1 9 (d) 10 2 10
4
Q30. The probability of selecting a male or a female is same. If the probability that in an office of
persons
n 1 males being selected is
(a) 6
(b) 8
3 10
2
, the value of
n
n
is:
(c) 10
(d) 12
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ANSWERS
1. c
2. d
3. c
4. b
5. a
6. d
7. d
8. a
9. c
10. a
11. c
12. b
13. a
14. b
15. b
16. c
17. c
18. c
19. a
20. c
21. d
22. b
23. b
24. b
25. b
26. c
27. c
28. a
29. d
30. d
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