DEPARTMENT OF APPLIED STATISTICS & DATA ANALYTICS
F.Y.B.Sc. USMAAS102
PROBABILITY AND PROBABILITY DISTRIBUTION
Practical No.:3. Date: / /2022
1. A man has 5 one rupee coins and one of them is known to have two
heads. He selects one coin at random and tosses it 5 times. If it always
falls head upwards, what is the probability that it is the coin with two
heads?
2. Two archers A and B take turns to shoot an apple, with A starting. When
A shoots the probability that his arrow hits the apple is 0.2 and when
B shoots the probability that his arrow hits the apple is 0.25. Find the
probability that B is the first to hit the apple.
3. A student applies for membership to a Hiking Club and also to the
Nature Club. The probability that he is accepted by the Hiking Club is
0.6, the probability that he is accepted by the nature Club is 0.7, and
the probability that he is not accepted by either club is 0.25. Find the
probability that
(i) He is accepted by both clubs;
(ii) He is accepted by the Hiking club but not by the Nature club;
(iii) He is accepted by the Hiking club given that he is accepted by the
Nature club;
4. The members of a consulting firm rent cars from three rental agencies:
60 percent from agency 1, 30 percent from agency 2, and 10 percent
from agency 3. If 9 percent of the cars from agency 1 need an oil change,
20 percent of the cars from agency 2 need an oil change, and 6 percent
of the cars from agency 3 need an oil change, what is the probability
that a rental car delivered to the firm will need an oil change?
If a rental car delivered to the consulting firm needs an oil change, what
is the probability that it came from rental agency 2?
5. A life insurance company issues standard, preferred, and ultra-
preferred policies. Of the company’s policyholders of a certain age, 60%
are standard with a probability of 0.01 of dying in the next year, 30%
preferred with a probability of 0.008 of dying in the next year, and 10%
are ultra-preferred with a probability of 0.007 of dying in the next year.
A policyholder of that age dies in the next year. What are the conditional
probabilities of the deceased being standard, preferred, and ultra-
preferred?
FOR PRACTICE
F.Y.B.Sc. USMAAS102
PROBABILITY AND PROBABILITY DISTRIBUTION
Practical No.:3. Date: / /2022
1. A man has 5 one rupee coins and one of them is known to have two
heads. He selects one coin at random and tosses it 5 times. If it always
falls head upwards, what is the probability that it is the coin with two
heads?
2. Two archers A and B take turns to shoot an apple, with A starting. When
A shoots the probability that his arrow hits the apple is 0.2 and when
B shoots the probability that his arrow hits the apple is 0.25. Find the
probability that B is the first to hit the apple.
3. A student applies for membership to a Hiking Club and also to the
Nature Club. The probability that he is accepted by the Hiking Club is
0.6, the probability that he is accepted by the nature Club is 0.7, and
the probability that he is not accepted by either club is 0.25. Find the
probability that
(i) He is accepted by both clubs;
(ii) He is accepted by the Hiking club but not by the Nature club;
(iii) He is accepted by the Hiking club given that he is accepted by the
Nature club;
4. The members of a consulting firm rent cars from three rental agencies:
60 percent from agency 1, 30 percent from agency 2, and 10 percent
from agency 3. If 9 percent of the cars from agency 1 need an oil change,
20 percent of the cars from agency 2 need an oil change, and 6 percent
of the cars from agency 3 need an oil change, what is the probability
that a rental car delivered to the firm will need an oil change?
If a rental car delivered to the consulting firm needs an oil change, what
is the probability that it came from rental agency 2?
5. A life insurance company issues standard, preferred, and ultra-
preferred policies. Of the company’s policyholders of a certain age, 60%
are standard with a probability of 0.01 of dying in the next year, 30%
preferred with a probability of 0.008 of dying in the next year, and 10%
are ultra-preferred with a probability of 0.007 of dying in the next year.
A policyholder of that age dies in the next year. What are the conditional
probabilities of the deceased being standard, preferred, and ultra-
preferred?
FOR PRACTICE
