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Chapter 11: Problem 56
Find the number of different signals consisting of nine flags that can be made using three white flags, five red flags, and one blue flag.
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If the expected value of a game is negative, what does this mean? Also describe the meaning of a positive and a zero expected value.
Involve computing expected values in games of chance. Another option in a roulette game (see Example 6 on page 753 ) is to bet \(\$ 1\) on red. (There are 18 red compartments, 18 black compartments, and 2 compartments that are neither red nor black.) If the ball lands on red, you get to keep the \(\$ 1\) that you paid to play the game and you are awarded \(\$ 1\). If the ball lands elsewhere, you are awarded nothing and the \(\$ 1\) that you bet is collected. Find the expected value for playing roulette if you bet \(\$ 1\) on red. Describe what this number means.
A restaurant offers the following limited lunch menu. $$ \begin{array}{|l|l|l|l|} \hline \text { Main Course } & \text { Vegetables } & \text { Beverages } & \text { Desserts } \\ \hline \text { Ham } & \text { Potatoes } & \text { Coffee } & \text { Cake } \\\ \hline \text { Chicken } & \text { Peas } & \text { Tea } & \text { Pie } \\ \hline \text { Fish } & \text { Green beans } & \text { Milk } & \text { Ice cream } \\ \hline \text { Beef } & & \text { Soda } & \\ \hline \end{array} If one item is selected from each of the four groups, in how many ways can a meal be ordered? Describe two such orders. $$
Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. An apartment complex offers apartments with four different options, designated by A through D. There are an equal number of apartments with each combination of options. $$ \begin{array}{|l|l|l|l|} \hline \text { A } & \text { B } & \text { C } & \text { D } \\ \hline \text { one bedroom } & \text { one } & \text { first } & \text { lake view } \\ \text { two bedrooms } & \text { bathroom } & \text { floor } & \text { golf course } \\ \text { three } & \text { two } & \text { second } & \text { view } \\ \text { bedrooms } & \text { bathrooms } & \text { floor } & \text { no special } \\ & & & \text { view } \\ \hline \end{array} $$ If there is only one apartment left, what is the probability that it is precisely what a person is looking for, namely two bedrooms, two bathrooms, first floor, and a lake or golf course view?
Consider a political discussion group consisting of 5 Democrats, 6 Republicans, and 4 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting no Independents.
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