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Chapter 11: Problem 28
Evaluate each expression. \(\frac{{ }_{5} C_{1} \cdot{ }_{7} C_{2}}{{ }_{12} C_{3}}\)
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Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. The Fundamental Counting Principle can be used to determine the number of ways of arranging the numbers \(1,2,3,4,5, \ldots, 98,99,100\)
There are three highways from city \(A\) to city \(B\), two highways from city \(B\) to city \(C\), and four highways from city \(C\) to city \(D\). How many different highway routes are there from city A to city D?
Nine cards numbered from 1 through 9 are placed into a box and two cards are selected without replacement. Find the probability that both numbers selected are odd, given that their sum is even.
Are related to the SAT, described in Check Point 4 on page \(752 .\) A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of \(\$ 300,000\) if successful and a yearly loss of \(\$ 100,000\) otherwise. The probability of success is \(\frac{1}{2}\). If the second mall is selected, it is estimated that the yearly profit will be \(\$ 200,000\) if successful; otherwise, the annual loss will be \(\$ 60,000\). The probability of success at the second mall is \(\frac{3}{4}\). Which mall should be chosen in order to maximize the expected profit?
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 HOMEOWNERS' INSURANCE CLAIMS $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Amount of Claim (to the } \\ \text { nearest } \$ \mathbf{\$ 5 0 , 0 0 0 )} \end{array} & \text { Probability } \\ \hline \$ 0 & 0.65 \\ \hline \$ 50,000 & 0.20 \\ \hline \$ 100,000 & 0.10 \\ \hline \$ 150,000 & 0.03 \\ \hline \$ 200,000 & 0.01 \\ \hline \$ 250,000 & 0.01 \\ \hline \end{array} $$
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