91Ó°ÊÓ

PROBLEM SOLVING At a school, \(43 \%\) of students attend the homecoming football game. Only \(23 \%\) of students go to the game and the homecoming dance. What is the probability that a student who attends the football game also attends the dance?

You flip a coin three times. It lands on heads twice and on tails once. Your friend concludes that the theoretical probability of the coin landing heads up is \(P\) (heads up) \(=\frac{2}{3}\). Is your friend correct? Explain your reasoning.

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?

Compare two-way tables and Venn diagrams. Then describe the advantages and disadvantages of each.

A company creates a new snack, \(\mathrm{N}\), and tests it against its current leader, L. The table shows the results. $$ \begin{array}{|l|c|c|} \hline & \text { Prefer L } & \text { Prefer N } \\ \hline \text { Current L Consumer } & 72 & 46 \\ \hline \text { Not Current L Consumer } & 52 & 114 \\ \hline \end{array} $$ The company is deciding whether it should try to improve the snack before marketing it, and to whom the snack should be marketed. Use probability to explain the decisions the company should make when the total size of the snack's market is expected to (a) change very little, and (b) expand very rapidly.

PROBLEM SOLVING You and 19 other students volunteer to present the "Best Teacher" award at a school banquet. One student volunteer will be chosen to present the award. Each student worked at least 1 hour in preparation for the banquet. You worked for 4 hours, and the group worked a combined total of 45 hours. For each situation, describe a process that gives you a "fair" chance to be chosen, and find the probability that you are chosen. a. "Fair" means equally likely. b. "Fair" means proportional to the number of hours each student worked in preparation.

A manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Predict the number of computers with defects in a shipment of 15,000 computers. Explain your reasoning.

Draw a Venn diagram of the sets described. Of the positive integers less than 15 , set \(A\) consists of the factors of 15 and set \(B\) consists of all odd numbers.

MODELING WITH MATHEMATICS A football team is losing by 14 points near the end of a game. The team scores two touchdowns (worth 6 points each) before the end of the game. After each touchdown, the coach must decide whether to go for 1 point with a kick (which is successful \(99 \%\) of the time) or 2 points with a run or pass (which is successful \(45 \%\) of the time). a. If the team goes for 1 point after each touchdown, what is the probability that the team wins? loses? ties? b. If the team goes for 2 points after each touchdown, what is the probability that the team wins? loses? ties? c. Can you develop a strategy so that the coach's team has a probability of winning the game that is greater than the probability of losing? If so, explain your strategy and calculate the probabilities of winning and losing the game.

Evaluate the expression. \({ }_{15} C_8\)