Q: Are the events 'being a Republican' and 'opposing the death penalty' independent? Use the table to justify your answer.

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

Q: If $$P(A) = 0.52$$, $$P(B) = 0.23$$, and $$P(A \cap B) = 0.07$$, are events A and B independent?

No, because $$P(A \cap B) \neq P(A) \cdot P(B)$$

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

$$0.62 + 0.25 - (0.62 \times 0.25) = 0.735$$

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?

$$\frac{7}{12} \times \frac{6}{11} = \frac{42}{132} = 0.318$$

Question 1

Which region is represented by the green area in the Venn diagram shown?

Accepted Answer

$$A^c \cap B^c$$

Question 2

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

Accepted Answer

$$0.04 + 0.24 + 0.10 = 0.38$$

Question 3

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

Accepted Answer

$$0.04$$

Question 4

Are the events 'being a Republican' and 'opposing the death penalty' independent? Use the table to justify your answer.

Accepted Answer

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

Question 5

If $$P(A) = 0.52$$, $$P(B) = 0.23$$, and $$P(A \cap B) = 0.07$$, are events A and B independent?

Accepted Answer

No, because $$P(A \cap B) 
eq P(A) \cdot P(B)$$

Question 6

A real estate ad states that 64% of homes have garages, 21% have pools, and 17% have both. What is the probability that a home has a pool or a garage?

Accepted Answer

$$0.64 + 0.21 - 0.17 = 0.68$$

Question 7

Using the same real estate data, what is the probability that a home has neither a pool nor a garage?

Accepted Answer

$$1 - 0.68 = 0.32$$

Question 8

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

Accepted Answer

$$0.62 + 0.25 - (0.62 	imes 0.25) = 0.735$$

Question 9

If the probability that a person drinks coffee is $$0.62$$ and eats bagels is $$0.25$$, what is the probability that a person does NOT drink coffee nor eat bagels?

Accepted Answer

$$1 - 0.735 = 0.265$$

Question 10

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

$$\frac{7}{12} 	imes \frac{6}{11} = \frac{42}{132} = 0.318$$

Question 11

Suppose 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 either Canada or Mexico?

Accepted Answer

$$0.18 + 0.09 - 0.04 = 0.23$$

Question 12

Using the same travel data, what is the probability that a resident has traveled to Canada but not Mexico?

Accepted Answer

$$0.18 - 0.04 = 0.14$$

Question 13

If $$P(A) = 0.45$$, $$P(B) = 0.11$$, and $$P(A \cap B) = 0$$, what can you conclude about events A and B?

Accepted Answer

They are mutually exclusive.

Question 14

A candy machine produces 20% red, 50% blue, and 30% green M&Ms. What is the probability that the first two M&Ms you pick are green?

Accepted Answer

$$0.3 	imes 0.3 = 0.09$$

Question 15

A shelter has 18 cats, 6 of which are male. What is the probability that a pet is male, given that it is a cat?

Accepted Answer

$$\frac{6}{18} = 0.333$$

Question 16

A shelter has 24 dogs (8 male) and 18 cats (6 male). What is the probability that a pet is female, given that it is a dog?

Accepted Answer

$$\frac{16}{24} = 0.667$$

Question 17

If $$P(B|A) = P(B)$$, what does this imply about events A and B?

Accepted Answer

A and B are independent.

Guided Practice: Independent and Dependent Probability in Introductory Statistics

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