4. Probability

Suppose that two cards are randomly selected from a standard 52-card deck.

b. What is the probability that the first card is a king and the second card is a king if the sampling is done with replacement?

Independent?

Refer to the contingency table in Problem 17 that relates age and likelihood to buy American. Determine P(45–54 years old) and P(45–54 years old | more likely). Are the events "45–54 years old" and "more likely" independent?

Marriage and Education

According to the U.S. Census Bureau, 20.2% of American women aged 25 years or older have a Bachelor's Degree. 16.5% have never married. Among women 25 years or older who have never married, 22.8% have a Bachelor's Degree. Among women 25 years or older who have a Bachelor's Degree, 18.6% have never married.

a. Are the events "have a Bachelor's Degree" and "never married" independent? Explain.

Suppose that P(E) = 0.8, P(F) = 0.5, and P(E and F) = 0.24. Are events E and F independent? Why?

Traffic Fatalities

In 2016, there were 34,439 traffic fatalities in the United States, with 9,477 of them being alcohol related.

d. What is the probability that neither of two randomly selected traffic fatalities in 2016 were alcohol related?

During the 2018 season, the Chicago Cubs won 58% of their games. Assuming game outcomes are independent and the win percentage remains the same for this season, answer the following:

b. What is the probability that the Cubs will win seven consecutive games?