UNIT 3 INTRODUCTION TO PROBABILITY
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QUESTIONS
1.A manufacturing company employs three analytical plans for the design and development of a
particular product. For cost reasons, all three are used at varying times. In facts, plan 1,2 and 3 are used
for 30%, 20% and 50% of the products respectively. The defect rate in different procedures is as follows:
P(D/P1 ) = 0.01, P(D/P2 ) = 0.03, P(D/P3 )= 0.02, where P(D/PJ ) is the probability of a defective product,
given plan j. If a random product was observed and found to be defective, which plan was most likely
used and thus responsible?
2. Write short notes on
a. Conditional probability
b. Bayes Theorem
c. Addition Theorem of Probability
d. Multiplication Law of Probability
3. A factory produces a certain type of output by three types of machines. the respective daily
production figures are Machine-I:3000 units, Machine-II:2500 units, Machine-III:4500 units. past
experience shows that 3% of the output produced by machine-I is defective. The corresponding fraction
of defectives for the other two machines are 1.2% and 2% respectively. An item is drawn at random from
the day`s production and is found to be defective. what is the probability that it comes from the output
of (i)machine-I (ii) machine-II (iii) machine-III?
4 What is the probability that a couple`s second child will be
(a) a boy, given that their first child was a girl.
(b) a girl, given that their first child was a girl.
5.From a pack of 52 cards 2 cards are drawn at random. find the probability that (i)one is king and other
is queen (ii) both are face cards (iii) one is spade and other is club.
6. The probability that A can solve a problem in programming is 4/5, B can solve it is 2/3 and C can it is
3/7. if all of them try independently, find the probability that
(a) problem will be solved
(b) Only one of them can solve the problem.
(c) non of them will solve the problem.
(d) A solves it but B and C cannot.
(e) All three students A,B and C can solve the problem.
7.What is the probability that a leap year selected at random contain 53 Saturdays ?
8.The chances of X,Y,Z becoming manager of a worldlink pvt.ltd are 4:2:3. The probabilities that
bonus to the staff will be introduced if X,Y,Z becoming manager are 0.3,0.5 and 0.8 respectively.
If the bonus scheme has been introduced, what is the probability that X is appointed as the
manager?
9.In tossing a coin three times, find the probability of getting (i) no heads (ii) Two heads (iii) at
least Two heads.
10.The odds against solving a problem by B is 4 to 3. The odds in favor of solving the same
problem by A is 7 to 6. What is the probability that problem will be solved if both of them try
independently ?
11.Urn A contains 2 white, 1 black and 3 red balls, urn B contains 3 white,2 black and 4 red balls
and urn C contains 4 white, 3 black and 2 red balls . one urn is chosen at random and 2 balls are
drawn, they happen to be red and black. What is the probability that both balls come from urn B?
12.A factory has 3 units A,B and C . A produces 25% of its products, unit B produces 25% and
the unit C produces 50% . If the percentage of defective items produced by three units A,B and C
respectively 1%,2% and 3% and an item selected randomly from the total production of the
factory is found to be defective, What is the probability that it is produced by the unit C ?