MAT 107
Probability Practice Problems Work Sheet 3
Directions: Please read and answer each question carefully. Round answers to 3 decimal places
where applicable.
1. Let P(A) = 0.4, P(B) = 0.2, and P( A | B) = 0.6
a. Find P (A ∩ B)
b. Find P (B | A)
c. Find P(A U B)
d. Are A and B independent? Justify!
2. In the state of Idaho, license plates consist of 3 capital letters and 3 digits.
a. How many license plates are possible?
b. What is the probability that a random plate begins with the letter X?
c. What is the probability that a random plate begins with the letter X and ends in a 9?
3. There are 15 members of the senate available for a committee, 9 are Male and 6 are
Female. The committee will have 5 people. Suppose the committee is selected at
random.
a. Find the probability that the committee consists of 5 Males.
b. Find the probability that the committee has at least 1 Female.
c. Find the probability that the committee consists of 3 Males and 2 Females.
d. If the committee consisted of all Females, would you believe the committee was
selected at random? Justify.
4. The following table gives data for a survey given to 100 random commuters and 100
random resident students asking about satisfaction with the university. A random
student is selected. Find:
a. The probability that the student is a resident given he/she had a high satisfaction.
b. The probability that the student had a high satisfaction given he/she is a resident
c. Are being a resident and having a high satisfaction independent? Justify
Resident
Commuter
Low
12
48
Middle
30
42
High
58
10
5. In a certain rural area of New York state, 80% of drivers use chains on the car tires for
winter driving. 60% of drivers carry a snow shovel in their car and use chains on their car
tires. 15% of drivers carry a shovel and do not use chains on their tires. A random driver
from this area is selected.
a. Find the probability that they carry a shovel, given they use chains.
b. Given the person does not use chain, find the probability that they carry a shovel.
c. Find the probability that the person uses chains or carries a shovel.
6. During frequent trips to a certain city, a female traveling salesperson stays at hotel A
50% of the time, at hotel B 30% of the time and at hotel C 20% of the time. When
checking in, there is some problem with the reservation 3% of the time at hotel A, 6% of
the time at hotel B and 10% of the time at hotel C. Suppose the salesperson travels to
this city.
a. Find the probability that she stays at hotel A and has a reservation problem.
b. Find the probability that she has a problem with the reservation.
c. Suppose that she has a problem with the reservation, find the probability that she is
staying at hotel A.
7. Acme Rental Cars has 10 Foreign cars and 6 American cars. If you choose 5 cars at
random, find and label the probability that:
a. Exactly 3 chosen cars are Foreign.
b. All the chosen cars are Foreign.
c. None of the chosen cars are Foreign.
d. Exactly 1 chosen car is Foreign.
e. At least 1 chosen car is Foreign.
f. At most 4 chosen cars are Foreign.
g. At least 2 chosen cars are Foreign.
8. A teacher is giving an exam where students will have to answer 4 essay questions. She
gives the students 12 possible essay questions the week before the exam. A specific
student, Bob, only has time to prepare for 7 of the questions.
a.
b.
c.
d.
e.
Find the probability that Bob has prepared for all the essays on the test.
Find the probability that Bob has prepared for exactly 3 of the essays on the test.
Find the probability that Bob has prepared for none of the essays on the test.
Find the probability that Bob has prepared for at least 1 of the essays on the test.
Find the probability that Bob has prepared for at least 2 of the essays on the test.