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

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

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

$$\frac{7}{12} \times \frac{6}{11}$$

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 if these events are independent?

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

Question 1

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

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

$$0.38$$

Question 3

Given the death penalty table, what is the probability that a randomly chosen 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 $$P(	ext{Republican} \cap 	ext{Oppose}) 
eq P(	ext{Republican}) \cdot P(	ext{Oppose})$$

Question 5

If $$P(A) = 0.52$$, $$P(B) = 0.23$$, and $$P(A \cap B) = 0.07$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.68$$

Question 6

Suppose the probability that a home has a garage is $$0.64$$, a pool is $$0.21$$, and both is $$0.17. $$What is the probability that a home has neither a pool nor a garage?

Accepted Answer

$$0.32$$

Question 7

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

Accepted Answer

$$0.285$$

Question 8

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

Accepted Answer

$$0.09$$

Question 9

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

Accepted Answer

$$\frac{7}{12} 	imes \frac{6}{11}$$

Question 10

Suppose $$P(A) = 0.18$$, $$P(B) = 0.09$$, and $$P(A \cap B) = 0.04. $$What is the probability that a person has traveled to Canada but not Mexico?

Accepted Answer

$$0.14$$

Question 11

In a shelter with 24 dogs and 18 cats (8 dogs and 6 cats are male), what is the probability that a pet is male, given that it is a cat?

Accepted Answer

$$\frac{6}{18}$$

Question 12

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

Accepted Answer

A and B are independent

Question 13

If you select 4 potential blood donors, each with a $$45\%$$ chance of being Type O, what is the probability all are Type O?

Accepted Answer

$$0.45^4$$

Question 14

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 if these events are independent?

Accepted Answer

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

Question 15

A university requires biology majors to take either Statistics or a computer course. If $$52\%$$ have taken Statistics, $$23\% a $$computer course, and $$7\%$$ both, what is the probability a student has taken neither?

Accepted Answer

$$1 - [0.52 + 0.23 - 0.07]$$

Independent and Dependent Probability: Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards