PROBABILITY (Board Paper Questions 2008-2012)
1. A fair die is rolled. If 1 turns up, a ball is picked at random from bag A, if 2 or 3 turn up,
a ball is picked from bag B, otherwise a ball is picked from C.Bag A has 3 red and 2
white balls, bag B has 3 red and 4 white and bag C has 4 red and 5 white.Tha die is rolled,
a bag is picked up and a ball is drawn.If the ball is red, what is the probabilitythat bag B
was picked?
Ans: [
]
2. Three ball are drawn without replacement from a bag with 5 white and 4 green balls. Find
the probability distribution of number of green balls drawn.
X
P(X)
0
1
2
3
Ans:
3. Let X denote the number of hours you study on any day. Probability that X can take
values x, has the following form where k is some constant,
P(X = x) =
Find: (i) value of k
(ii) Probability you study-(a) At least 2 hours
(b) Exactly 2 hours
(c) At most 2 hours
Ans:[ 0.15, 0.75, 0.3 ,0.55]
4. In answering a multiple choice test , a student either knows the answer or guesses. Let
be the probability he knows the answer ,
be the probability he guesses. Assuming that a
student who guesses will be correct with probability what is the probability that the
student knows the answer, given he answered it correctly.
Ans:[
]
5. A bag contains 4 balls.2 balls are drawn at random and are found to be white. What is the
probability that all are white?
Ans: [ ]
6. An urn contains 4 white and 3 red balls. Let X be the number of red balls in a random
draw of 3 balls. Find the mean and variance of X.
Ans: [ ,
]
7. Bag I contains 4 white, 3 red and Bag II contains 3 white , 7 red. One ball is drawn from
one of the bags and id found to be white. Find the probability that it was drawn from Bag
I?
Ans: [
]
8. From a lot of 10 bulbs, which includes 3 defectives , a sample of 2 bulbs is drawn at
random. Find the probability distribution of number of defective bulbs.
X
0
1
2
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P(X)
Ans :
9. A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the
probability distribution of number of successes and its mean.
X
P(X)
Ans:
0
1
2
3
4
Mean :
10. Ina college 4% of boys and 1% of girls are taller than 1.75m. Further 60% of the students
are girls. A student is selected at random from the college and is found to be taller than
1.75m. Find the probability that the selected student is a girl.
Ans: [
]
11. Two bags A and B contain 4 white and 3 black balls and 2 white and 2 black balls
respectively. From Bag A , 2 balls are drawn and transferred to bag B. A ball is the drawn
from bag B and is found to be a black ball. What is the probability that the transferred
balls were 1 white and 1 black.
Ans: [
]
12. In an exam,10 questions of true-false type are asked. A student tosses a fair coin. If coin
falls heads, he answers true and if it falls tails he answers false. Show that the probability
that he answers at most 7 questions correctly is
.
13. A biased dice is twice as likely to show an even number as an odd number. The die is
rolled three times. If occurrence of an even number is considered a success, write the
probability distribution of number of successes. Also find mean.
Ans: X
0
1
2
3
P(X)
Mean : 2
14. A and B throw a pair of dice turn by turn. The first to throw a 9 is awarded a prize. If A
starts the game, show that the probability of A getting a prize is
.
15. Probability of a man hitting a target is . How many times must he fire so that probability
of hitting the target at least once is greater than
16. Probability that A hits a target is
and B hits
?
Ans : [ At least 4 times ]
.If each shoots, what is the probability
that (i) target is hit? (ii) exactly one of them hits the target?
Ans: [
,
]
17. A die is thrown again and again till 3 sixes are obtained. What is the probability of getting
the third six in the sixth throw of the die?
Ans: [
]
18. Bag I and Bag II have 3 red,4 black and 4 red, 5 black balls respectively. One ball is
transferred from Bag I to Bag II and then a ball is drawn fromm Bag II. Find the
probability that the transferred ball is black?
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Ans: [
]
19. A man is known to speak truth 3 out of 4 times. He throws a die and reports a six. Find
the probability that it is actually a six. Ans: [
]
20. A card from a pack of 52 cards is lost. From the rest 2 cards are drawn at random and are
found to be clubs. Find the probability of the lost card being a club?
Ans: [
]
21. Bag A has 4 white and 3 black balls , Bag B has 2 white and 2 black balls. From Bag A, 2
balls are transferred to Bag B. Find the probability of drawing
(a) 2 white balls from Bag B
(b) 2 black balls from Bag B
(c) 1 white and 1 black ball from Bag B
Ans: [
,
,
]
22. A letter is known to have come either from TATANAGAR or CALCUTTA. On the
envelope 2 consecutive letters TA are visible. What is the probability the letter came from
(i)
CALCUTTA
(ii) TATANAGAR
Ans: [
,
]
23. A factory has 2 machines A and B. Past record shows A produced 60% of items and B
produces 40%. Further 2% of items by A and 1% by B were defective. All items are put
into one stockpile and then 1 item is chosen at random.It is found to be defective. What is
the probability that B produced it?
Ans: [
]
24. 3 coins, one is 2 headed coin, one is biased that comes up with tail 25% of the time and
on unbiased. One coin is chosen and tossed. It shoes heads. What is the probability that it
was a 2 headed coin?
Ans: [ ]
25. A2 cards are drawn without replacement from a pack of 52 cards. Find the probability
distribution of the number of kings.
Ans:
X
P(X)
0
1
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