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

Bowling

Suppose that Ralph gets a strike when bowling 30% of the time.

a. What is the probability that Ralph gets two strikes in a row?

Audits and Pet Ownership

According to Internal Revenue Service records, 6.42% of all household tax returns are audited. According to the Humane Society, 39% of all households own a dog. Assuming dog ownership and audits are independent events, what is the probability a randomly selected household is audited and owns a dog?

Betting on Sports

According to a Gallup Poll, about 17% of adult Americans bet on professional sports. Census data indicate that 48.4% of the adult population in the United States is male.

d. How will the information in part (c) affect the probability you computed in part (b)?

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.

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?

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.

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?