4. Probability

Suppose that you roll a pair of dice 1000 times and get seven 350 times. Based on these results, what is the probability that the next roll results in seven?

Explain what is meant by a subjective probability. List some examples of subjective probabilities.

Playing Five-Card Stud

In the game of five-card stud, each player is dealt one card face down and four cards face up. After two cards are dealt (one down, one up), players bet, and betting continues after each additional card is dealt. Suppose three cards have been dealt to each of five players at the table. You currently have three clubs and are trying to get a flush (all cards of the same suit). Of the cards dealt, two clubs are visible in other players' hands.

e. Should you continue playing the game?

Mark McGwire

During the 1998 Major League Baseball season, Mark McGwire of the St. Louis Cardinals hit 70 home runs. Out of these, 34 went to left field, 20 to left center, 13 to center field, 3 to right center, and 0 to right field. (Source: Miklasz, B., et al. Celebrating 70: Mark McGwire’s Historic Season, Sporting News Publishing Co., 1998, p. 179.)

b. What is the probability that a randomly chosen home run went to right field?

Lottery Luck In 1996, a New York couple won \$2.5 million in the state lottery. Eleven years later, the couple won \$5 million in the state lottery using the same set of numbers. The odds of winning the New York lottery twice are roughly 1 in 16 trillion, described by a lottery spokesperson as “galactically astronomical.” Although it is highly unlikely that an individual will win the lottery twice, it is not “galactically astronomical” that someone will win a lottery twice. Explain why this is the case.

Coffee Sales The following data represent the number of cases of coffee or filters sold by four sales reps in a recent sales competition.

b. What is the probability that a randomly chosen case was Gourmet?

a. Patti and John each played 100 games of Solitaire on their smartphones. Patti won 7 games and estimated her probability of winning Solitaire as 0.07. John won 6 games and estimated his probability as 0.06. Why do their estimates differ?

b. Would an empirical probability based on 100 games or 1000 games give a better estimate of the probability of winning Solitaire? Why?

The following represent the results of a survey in which individuals were asked to disclose what they perceive to be the ideal number of children.

b. What is the probability an individual is female and believes the ideal number of children is 2?

In Pennsylvania’s Cash 5 lottery, balls are numbered 1 to 43. Five balls are selected randomly, without replacement. The order in which the balls are selected does not matter. To win, your numbers must match the five selected. Determine your probability of winning Pennsylvania’s Cash 5 with one ticket.

"Putting It Together: Red-Light Cameras

In a study of the feasibility of a red-light camera program in the city of Milwaukee, the data below summarize the projected number of crashes at 13 selected intersections over a five-year period.

(g) Based on the data shown, does it appear that the red-light camera program will be beneficial in reducing crashes at the intersections? Explain.

"

[NW] [DATA] TelevisionsIn the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.

e. What is the probability that a randomly chosen household has three televisions?