AP Statistics Name______
Probability Review Worksheet
1. Explain why the following quotation is not true:
“What I think is our best determination is it will be a colder than normal winter,” said Pamela Knox, a Wisconsin state climatologist. “I’m basing that on a couple of different things. First, in looking at the past few winters, there has been a lack of really cold weather. Even though we are not supposed to use the law of averages (a.k.a. Law of Large Numbers), we are due.” (Associated Press, fall 1992, quoted by Schaeffer et al.)
2. The plastic arrow on a spinner for a child’s game stops rotating to point at a color that will determine what happens next. Which of the following probability assignments for getting each color on a spin are possible?
P(red) / P(yellow) / P(green) / P(blue)A) / 0.25 / 0.25 / 0.25 / 0.25
B) / 0.1 / 0.2 / 0.3 / 0.4
C) / 0.2 / 0.3 / 0.4 / 0.5
D) / 0 / 0 / 1 / 0
E) / 0.1 / 0.2 / 1.2 / -1.5
3. A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need to be repaired twice, and 4% will require three or more repairs.
a. What is the probability that a car chosen at randon will need
· No repairs?
· No more than one repair?
· Some repairs?
b. If you own two cars, what is the probability that
· Neither will need repair?
· Both will need repair?
4. 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 are divisible by 3?
d. you roll at least one 5?
e. the numbers you roll are not all 5’s?
5. Suppose that in your city 37% of the voters are registered as Democrats, 29% as Republicans, and 11% as members of other parties. Voters not aligned with any official party are termed “Independent.” You are conducting a poll by calling registered voters at random. In your first three calls, what is the probability that you talk to
a. all Republicans?
b. no Democrats?
c. at least one Independent?
6. You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities:
a. The card is a heart, given that it is red.
b. The card is red, given that it is a heart.
c. The card is an ace, given that it is red.
d. The card is a queen, given that it is a face card.
7. Suppose that 23% of adults smoke cigarettes. It’s known that 57% of smokers and 13% of nonsmokers develop a certain lung condition by age 60.
a. Explain how these statistics indicate that lung condition and smoking are not independent.
b. What’s the probability that a randomly selected 60-year old has this lung condition?
8. Explain the difference between combination and permutation.
9. The starting line-up for a baseball team consists of nine players. How many different batting orders are possible using the starting line-up?
10. A building contractor is planning to develop a subdivision. The subdivision is to consist of six one-story houses, four two-story houses, and two split-level houses. In how many distinguishable ways can the houses be arranged?
11. A state’s department of transportation plans to develop a new section of interstate highways and
receives 16 bids for the project. The state plans to hire four of the bidding companies. How
many different combinations of four companies can be selected from the 16 bidding companies?
12. A jury consists of five men and seven women. Three are selected at random for an interview.
Find the probability that all three are men.