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AHLCON PUBLIC SCHOOL
ASSIGNMENT NO 13
CLASS XII
Topic: PROBABILITY
1. If P(A) = 0.2, P(B) = p, P (AB) = 0.6 and A, B are given to be independent events,
find the value of p.
2. An Urn contains 4 red and 7 blue balls. Two balls are drawn at random with
replacement. Find the probability of getting
i) 2 red balls
ii) 2 blue balls
iii) one red and one blue ball.
3. A and B throw a pair of die turn by turn. The first to throw 9 is awarded a prize. If A
9
starts the game, show that the probability of “A” getting the prize is
.
17
4. There are two bags I and II. Bag I contains 2 white and 4 red balls and Bag II contains 5
white and 3 red balls. One ball is drawn at random from one of the bags and is found to
be red. Find the probability that it was drawn from bag II.
5. In a class having 70% boys, 20% of boys and 10% of the girls are players. A student is
selected at random from the class and is found to be a player. Find the probability that
the selected student is a girl.
6. A man is know to tell a lie 1 out of 4 times. He throws a die and reports that it is a six.
Find the probability that it is actually a six.
7. For A, B and C the chances of being selected as the manager of a firm are in the ratio 4:
1: 2 respectively. The respective probabilities for them to introduce a radical change in
marketing strategy are 0.3, 0.8 and 0.5. If the change does takes place, find the
probability that it is due to the appointment of B or C.
8. A pair of dice is tossed twice. If the random variable X is defined as the number of
doublets, find the probability distribution of X.
9. Two cards are drawn successively with replacement from a well – shuffled deck of 52
cards. Find the probability distribution of the number of jacks.
10. Four bad oranges are mixed accidentally with 16 good oranges. Find the probability
distribution of the number of bad oranges in a draw of two oranges.
11. Find the mean and variance for the following probability distribution –
X
P(X)
0
1
6
1
1
2
2
3
10
3
1
30
12. Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Find the
mean and standard deviation of the number of kings.
13. An experiment succeeds twice as often as fails. Find the probability that in the next six
trials, there will be atleast four successes.
14. A pair of dice is thrown 6 times. Getting a total of 7 on the two dice is considered a
success. Find the probability of getting: i) atleast 5 successes.
ii) exactly 5 successes
iii) atmost 5 successes iv) no success.
15. There are 6% defective items in a large bulk of items. Find the probability that a sample
of 8 items were include not more than one defective item.
16. If the mean and variance of a binomial distribution are respectively 9 and 6, find the
distribution.
17. If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, find the
distribution.
3
1
and that B solving it is . What is the
7
3
probability that i) atleast one of them solves the problem ii) only one of them will solve
the problem.
18. The probability of A solving a problem is
19. Ramesh appears for the interview for two posts A and B for which selection is
1
1
independent. . The probability of his selection for the post A is
and for post B is .
6
7
Find the probability that Ramesh is selected for atleast one of the post.
20. A problem in statistics is given to three students whose chances of solving it are
1 1 1
, , respectively. What is the probability that only one of them solves it correctly?
2 3 4