Party Affiliation
The following data represent political party by age from a random sample of registered Iowa voters.

b. Are the events "Democrat" and "65+" independent? Justify your answer.

A Random Process—The Lady Tasting Tea

Ronald Fisher is considered the father of experimental design. Being of English descent, he was having afternoon tea with a colleague. The colleague’s wife entered the room as Fisher was pouring tea. Fisher offered tea to the lady. She politely accepted and requested milk with her tea. Fisher started to pour milk into the tea cup first, but the lady indicated that she preferred her tea be poured first, then the milk. Fisher did not believe that the lady could tell the difference between “milk first” versus “milk second” tea, but the lady insisted she could tell the difference. Being the consummate scientist, Fisher suggested an experiment in which he randomly put milk into the tea first in some instances, and milk into the tea second in others. It turns out, the lady tasting tea was correct in all eight trials.

c. Explain how a coin could be used to simulate the random process of tasting eight cups of tea.

Rolling a Die What is the probability of obtaining 4 ones in a row when rolling a fair, six-sided die? Interpret this probability.

If P(E) = 0.6 and P(E|F) = 0.34, are events E and F independent?

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?