1. Find the probability distribution of number of doublets in three throws of a pair of dice.
2. A
fair coin is tossed 10 times. Find the probability of
a. Exactly six heads. b. At least six heads c. At most six heads.
3. Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack
of 52 cards. Find the mean, variance and standard deviation of the
number of kings.
4. From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random
with replacement. Find
the probability
distribution of the number of defective bulbs.
5. In a meeting 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take x = 0 if he opposed and x = 1 if he is in favour. Find E
(x) and var (x).
6. A laboratory blood test
is 99% effective in detecting a certain disease when it is in fact present. However
the test also yields a false positive result for 0.5% of the healthy person
tested (i.e. if a healthy person is tested then with probability 0.005, the
test will imply that he has the disease. If 0.1 percent of the population
actually has the disease, What is the probability that a person has the disease
given that the test result is positive ?
7. If P(A) = 0.2, P(B) = 0.3 and P (A U
B ) = 0.4, where a & b are two events associated with a random experiment. Find P (A ∩ B) and
P(A / B)
8. If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?
9. Bag I contain 3 red and 4 black balls and
bag
II contain 4 red and 5 black
balls. One ball is transferred from
Bag I to Bag II and then a
ball
is drawn from Bag
II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.
PAPER SUBMITTED: Mr.
PAWAN KUMAR JANGRA [ M.Sc. (math) , B.Ed., D.I.S.M , A.C.M]
Mob:
9464317615, 9888018092
E-Mail :
pkjangra2011@gmail.com
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