Q: Based on the death penalty table, what is the probability that a randomly chosen American voter OPPOSES the death penalty?

$$P(\text{Oppose}) = 0.04 + 0.24 + 0.10 = 0.38$$

Q: Given the death penalty table, what is the probability that a Republican voter OPPOSES the death penalty?

$$P(\text{Oppose} | \text{Republican}) = 0.04$$

Q: Are the events 'being a Republican' and 'opposing the death penalty' independent, based on the table?

No, because $$P(\text{Oppose} | \text{Republican}) \neq P(\text{Oppose})$$

Q: If the probability that a person drinks coffee is $$0.62$$ and the probability that a person eats bagels is $$0.25$$, what is the probability that a person drinks coffee OR eats bagels, assuming independence?

$$P(\text{Coffee} \cup \text{Bagels}) = 0.62 + 0.25 - (0.62 \times 0.25) = 0.765$$

Q: A university requires biology majors to take either a Statistics course or a computer course. 52% have taken Statistics, 23% have taken a computer course, and 7% have taken both. What is the probability that a randomly chosen biology major has taken NEITHER course?

$$P(\text{Neither}) = 1 - [0.52 + 0.23 - 0.07] = 0.32$$

Q: If 64% of homes for sale have garages, 21% have swimming pools, and 17% have both, what is the probability that a home has a pool but NO garage?

$$P(\text{Pool and no Garage}) = 0.21 - 0.17 = 0.04$$

Q: A junk box contains 12 batteries, 5 of which are dead. If you pick two batteries without replacement, what is the probability that BOTH are good?

$$P(\text{both good}) = \frac{7}{12} \times \frac{6}{11} = 0.318$$

Q: If the probability that a U.S. resident has traveled to Canada is $$0.18$$, to Mexico is $$0.09$$, and to both is $$0.04$$, what is the probability that a resident has traveled to Canada but NOT Mexico?

$$P(\text{Canada only}) = 0.18 - 0.04 = 0.14$$

Q: A candy machine produces 20% red, 50% blue, and 30% green M&Ms. If you pick 3 M&Ms at random, what is the probability that at least one is blue?

$$P(\text{at least one blue}) = 1 - (0.5)^3$ = 0.875$$

Question 1

Which formula correctly represents the probability that NEITHER event A nor event B occurs, as illustrated by the green region in the Venn diagram?

Accepted Answer

$$P(A^c \cap B^c) = 1 - P(A \cup B)$$

Question 2

Based on the death penalty table, what is the probability that a randomly chosen American voter OPPOSES the death penalty?

Accepted Answer

$$P(	ext{Oppose}) = 0.04 + 0.24 + 0.10 = 0.38$$

Question 3

Given the death penalty table, what is the probability that a Republican voter OPPOSES the death penalty?

Accepted Answer

$$P(	ext{Oppose} | 	ext{Republican}) = 0.04$$

Question 4

Are the events 'being a Republican' and 'opposing the death penalty' independent, based on the table?

Accepted Answer

No, because $$P(	ext{Oppose} | 	ext{Republican}) 
eq P(	ext{Oppose})$$

Question 5

If the probability that a person drinks coffee is $$0.62$$ and the probability that a person eats bagels is $$0.25$$, what is the probability that a person drinks coffee OR eats bagels, assuming independence?

Accepted Answer

$$P(	ext{Coffee} \cup 	ext{Bagels}) = 0.62 + 0.25 - (0.62 	imes 0.25) = 0.765$$

Question 6

A university requires biology majors to take either a Statistics course or a computer course. 52% have taken Statistics, 23% have taken a computer course, and 7% have taken both. What is the probability that a randomly chosen biology major has taken NEITHER course?

Accepted Answer

$$P(	ext{Neither}) = 1 - [0.52 + 0.23 - 0.07] = 0.32$$

Question 7

If 64% of homes for sale have garages, 21% have swimming pools, and 17% have both, what is the probability that a home has a pool but NO garage?

Accepted Answer

$$P(	ext{Pool and no Garage}) = 0.21 - 0.17 = 0.04$$

Question 8

A junk box contains 12 batteries, 5 of which are dead. If you pick two batteries without replacement, what is the probability that BOTH are good?

Accepted Answer

$$P(	ext{both good}) = \frac{7}{12} 	imes \frac{6}{11} = 0.318$$

Question 9

If the probability that a U.S. resident has traveled to Canada is $$0.18$$, to Mexico is $$0.09$$, and to both is $$0.04$$, what is the probability that a resident has traveled to Canada but NOT Mexico?

Accepted Answer

$$P(	ext{Canada only}) = 0.18 - 0.04 = 0.14$$

Question 10

A candy machine produces 20% red, 50% blue, and 30% green M&Ms. If you pick 3 M&Ms at random, what is the probability that at least one is blue?

Accepted Answer

$$P(	ext{at least one blue}) = 1 - (0.5)^3$ = 0.875$$

Question 11

In an animal shelter with 24 dogs (8 male) and 18 cats (6 male), what is the probability that a randomly selected pet is MALE, GIVEN that it is a cat?

Accepted Answer

$$P(	ext{Male} | 	ext{Cat}) = \frac{6}{18} = 0.333$$

Question 12

If you select 4 people at random from the US population (45% Type O, 40% Type A, 11% Type B, rest Type AB), what is the probability that NONE are Type AB?

Accepted Answer

$$P(	ext{no AB}) = (0.96)^4$ = 0.849$$

Question 13

Suppose you pick M&Ms one at a time from a machine that produces 30% green M&Ms. What is the probability that you have to pick 5 M&Ms to find the first green one?

Accepted Answer

$$P(	ext{first green at 5th}) = (0.7)^4$ 	imes 0.3 = 0.072$$

Question 14

If you select two batteries from a box of 12 (5 dead), what is the probability that the first is dead and the second is good?

Accepted Answer

$$P(	ext{dead, then good}) = \frac{5}{12} 	imes \frac{7}{11} = 0.265$$

Question 15

If the probability that a person drinks coffee is $$0.62$$ and the probability that a person eats bagels is $$0.25$$, what is the probability that a person does NOT drink coffee NOR eat bagels (assuming independence)?

Accepted Answer

$$P(	ext{neither}) = (1 - 0.62) 	imes (1 - 0.25) = 0.38 	imes 0.75 = 0.285$$

Independent and Dependent Probability: Study Notes for Introductory Statistics

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