91Ó°ÊÓ

The Redbirds trail the Bluebirds by one goal with 1 minute left in the hockey game. The Redbirds' coach must decide whether to remove the goalie and add a frontline player. The probabilities of each team scoring are shown in the table. $$\begin{array}{|c|c|c|}\hline & {\text { Goalie }} & {\text { No goalie }} \\\ \hline \text { Redbirds score } & {0.1} & {0.3} \\ \hline \text { Bluebirds score } & {0.1} & {0.6} \\ \hline\end{array}$$ a. Find the probability that the Redbirds score and the Bluebirds do not score when the coach leaves the goalie in. b. Find the probability that the Redbirds score and the Bluebirds do not score when the coach takes the goalie out. c. Based on parts (a) and (b), what should the coach do?

Complete the probability distribution for the random variable \(x\) . What is the probability the value of \(x\) is greater than 2 ? $$\begin{array}{|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} \\ \hline P(x) & {0.1} & {0.3} & {0.4} & {} \\ \hline\end{array}$$

Describe a real-life event that has a probability of 0. Then describe a real- life event that has a probability of 1.

Write a general rule for finding \(P(A \)or \(B\) or \(C)\) for (a) disjoint and (b) overlapping events \(A, B,\) and \(C .\)

Count the possible combinations of \(r\) letters chosen from the given list. (See Example 4 .) $$\mathrm{U}, \mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}, \mathrm{Z} ; r=3$$

Count the possible combinations of \(r\) letters chosen from the given list. (See Example 4 .) $$\mathrm{D}, \mathrm{E}, \mathrm{F}, \mathrm{G}, \mathrm{H} ; r=4$$

PROBLEM SOLVING At a gas station, 84\(\%\) of customers buy gasoline. Only 5\(\%\) of customers buy gasoline and a beverage. What is the probability that a customer who buys gasoline also buys a beverage?

MAKING AN ARGUMENT A meteorologist claims that there is a 70\(\%\) chance of rain. When it rains, there is a 75\(\%\) chance that your softball game will be rescheduled. Your friend believes the game is more likely to be rescheduled than played. Is your friend correct? Explain your reasoning.

Draw a Venn diagram of the sets described. Of the positive integers less than \(14,\) set \(A\) consists of all prime numbers and set \(B\) consists of all even numbers.

Draw a Venn diagram of the sets described. Of the positive integers less than \(24,\) set \(A\) consists of the multiples of 2 and set \(B\) consists of all the multiples of \(3 .\)