The main AP Statistics probability topics are: interpreting probability, the law of large numbers concept, addition rule,
multiplication rule, conditional probability and independence, discrete random variables and their probability distribution,
simulation of random behavior and probability distributions, mean and standard deviation of a random variable,
and linear transformation of a random variable.
Examples of AP Statistics multiple choice questions with probability calculations:
1. A box contains 3 yellow, 2 red, 4 green and 3 black marbles. Two marbles are taken one after the other at random from the box. What is the probability that both marbles are red?
a) 1/50 b) 1/60 c) 1/66 d) 2/57 e) 1/6
The probability that the first marble taken out of the box is red is 2/12 = 1/6.
The probability that the second marble taken out of the box is red is 1/11.
The probability of two red marbles taken out of the box is the product of 1/6 and 1/11. This is 1/66.
2. Four children are asked to pick their favorite ice cream flavor out of 8 different flavors, and each of them is equally likely to pick any of the eight ice cream flavors. What is the probability that each child orders a different ice cream type?
a) 100/149 b) 27/89 c) 63/128 d) 105/256 e) 66/97
P(A) = the probability of the first child choosing a flavor.
P(B) = the probability of the second child choosing a flavor different than the one chosen by the first child.
P(C) = the probability of the third child choosing a flavor different than the flavors chosen by the first two children.
P(D) = the probability of the fourth child choosing a flavor different than the flavors chosen by the other three children.
P(A and B and C and D) = P(A)·P(B | A)·P(C | A and B)·P(D | A and B and C).
P(A) = 8/8.
P(B | A) = 7/8.
P(C | A and B) = 6/8.
P(D | A and B and C) = 5/8.
P(A and B and C and D) = 105/256.
3. Six fruit baskets contain peaches, apples and oranges. Three of the baskets contain two apples and one orange each, two other baskets
contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random
and then select a fruit at random from the basket. Which of the following is the probability that the fruit is an apple?
a) .32 b) .4 c) .46 d) .5 e) .58
The probability of choosing an apple is:
(3 baskets/6 baskets)·(2 apples/3 fruits) + (2 baskets/6 baskets)·(3 apples/4 fruits) + (1 basket/6 baskets)·(0 apples/3 fruits) =
= 1/3 + 1/4 = .58.
4. A real estate agent finds home buyers and closes the sales for 70% of his clients that sell their homes.
What is the mean number of sales for his next 10 clients and what is the standard deviation of this distribution?
a) μ = 7 and σ = 1.45 b) μ = 7 and σ = 1.5 c) μ = 7 and σ = 1.2 d) μ = 7 and σ = 0 e) μ = 7 and σ = .66
The mean μ = 10·.7 = 7.
The standard deviation σ = √(10·.7·(1 - .7)) = 1.45.