Download Worksheet: (Probability)

Worksheet: (Probability)
1. What is the sample space and the sample points for the following:
a) Tossing 2 coins:
b) Rolling two dice:
c) Roll two dice and record the sum of the integers. (Are they equally likely?)
d) A deck of 52 playing cards:
2. A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired
once, 7% will need repairs twice and 4%will need three or more repairs. What is the probability
that a car chosen at random will need
a) No repair?
b) No more than one repair?
c) Some repairs?
If you own two cars, what is the probability that
a) Neither will need repair?
b) Both will need repair?
c) At least one car will need repair?
3. In a large Into Stats class the professor reports that 55% of the students that enroll have never
taken calculus, 32% have taken only one semester of calculus and the rest have taken two or more
semesters of calculus. The professor randomly assigns students to groups of three to work on a
project for the course. What is the probability that the first group mate you meet has studied
a) Two or more semesters of calculus?
b) Some calculus?
c) No more than one semester of calculus?
What is the probability that of your two group mates
a) Neither has studied calculus?
b) Both have studied at least one semester of calculus?
c) At least one had more than one semester of calculus?
4. A Gallup poll in March 2007 asked 1005 U.S adults whether increasing domestic energy
production or protecting the environment should be given higher priority. Here are the results:
Response
Number
Increase production
342
Protect environment
583
Equally important
30
No opinion
50
total
1005
If we select a person at random from this sample of 1005 adults,
a) What is the probability that the person responded “Increase Production”?
b) What is the probability that the person responded “Equally important “or had no opinion?
Suppose we select three people at random from this sample.
c) What is the probability that all three responded “Protect the environment”?
d) What is the probability that none responded “equally important”?
e) What is the assumption that you make while computing these probabilities?
5. The American Red Cross says that about 45% of the US population has Type O blood, 40% Type
A, 11% Type B and the rest Type AB.
a) Someone volunteers to give blood. What is the probability that this donor
1. Has Type AB blood?
2. Has Type A or Type B?
3. Is not Type O?
b) Among four potential donors, what is the probability that
1. All are Type O?
2. No one is Type AB?
3. They are not all Type A?
4. At least one person is Type B?
c) If you examine one person, are the events that the person is Type A and that the person is
type B disjoint (mutually exclusive), independent or neither?
d) If you examine two people, are the events that the first is Type A and the second Type B
disjoint, independent or neither?
6. You roll a fair die, three times. What is the probability that:
a) You roll all 6’s?
b) You roll all odd numbers?
c) None of your rolls gets a number divisible by 3?
d) You roll at least one 5?
e) The numbers that you roll are not all 5’s?
7. (Slightly harder) A junk box in your room contains a dozen old batteries, five of which are totally
dead. You start picking batteries one at a time and testing them. Find the probability of each
outcome.
a. The first two you choose are both dead.
b. At least one of the first three works.
c. The first four you pick all work.
d. You have to pick 5 batteries in order to find one that works.
8. A student is unprepared for a quiz which has seven multiple choice questions, each with five
possible answers. The student guesses the answer to each question, i.e., the student is equally
likely to choose any of the five possible answers, and chooses the answer to a question
independently of the answers chosen for the other questions.
a. What is the probability that the student answers Question 3 correctly?
b. What is the probability that the student gets all the questions wrong?
c. What is the probability that the student answers at least one question correctly?
d. What is the probability that the student answers either Question 1 or Question 2
correctly?
9. Real estate ads suggest that 64% of homes for sale have garages, 21% have swimming pools, and
17% have both features. What is the probability that a home for sale has
a. A pool or a garage?
b. Neither a pool nor a garage?
c. A pool but no garage?
d. If a home for sale has a garage, what’s the probability that it has a pool, too?
e. Are having a garage and pool independent events?
f.
Are having a garage and pool mutually exclusive events?
10. Employment data at a large company reveal that 72% of the workers are married, that 44% are
college graduates and that half of the college grads are married. What is the probability that a
randomly chosen worker
a. Is neither married nor a college graduate?
b. Is married but not a college graduate?
c. Is married or a college graduate?
11. Suppose the probability that a US resident has traveled to Canada is 0.18, to Mexico is 0.09, and
to both the countries is 0.04. What’s the probability that an American chosen at random has
a) Traveled to Canada but not to Mexico?
b) Traveled to either Canada or Mexico?
c) Not traveled to either country?