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Chapter 11: Problem 40
Use the formula for \({ }_{n} P_{r}\) to evaluate each expression. \({ }_{6} P_{0}\)
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Figure \(\mathbf{1 1 . 2}\) on page 689 shows that a tree diagram can be used to find the total number of outfits. Describe one advantage of using the Fundamental Counting Principle rather than a tree diagram.
The tables in Exercises 3-4 show claims and their probabilities for an insurance company. a. Calculate the expected value and describe what this means in practical terms. b. How much should the company charge as an average premium so that it breaks even on its claim costs? c. How much should the company charge to make a profit of \(\$ 50\) per policy? PROBABILITIES FOR MEDICAL INSURANCE CLAIMS $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Amount of Claim (to the } \\ \text { nearest } \mathbf{\$ 2 0 , 0 0 0 )} \end{array} & \text { Probability } \\ \hline \$ 0 & 0.70 \\ \hline \$ 20,000 & 0.20 \\ \hline \$ 40,000 & 0.06 \\ \hline \$ 60,000 & 0.02 \\ \hline \$ 80,000 & 0.01 \\ \hline \$ 100,000 & 0.01 \\ \hline \end{array} $$
An ice chest contains six cans of apple juice, eight cans of grape juice, four cans of orange juice, and two cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of grape juice.
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?
A restaurant offers the following limited lunch menu. $$ \begin{array}{|l|l|l|l|} \hline \text { Main Course } & \text { Vegetables } & \text { Beverages } & \text { Desserts } \\ \hline \text { Ham } & \text { Potatoes } & \text { Coffee } & \text { Cake } \\\ \hline \text { Chicken } & \text { Peas } & \text { Tea } & \text { Pie } \\ \hline \text { Fish } & \text { Green beans } & \text { Milk } & \text { Ice cream } \\ \hline \text { Beef } & & \text { Soda } & \\ \hline \end{array} If one item is selected from each of the four groups, in how many ways can a meal be ordered? Describe two such orders. $$
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