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Chapter 11: Problem 12

A committee of five people is to be formed from six lawyers and seven teachers. Find the probability that a. all are lawyers. b. none are lawyers.

Short Answer

Expert verified
a. The probability that all committee members are lawyers is approximately \(0.005\) (rounded to three decimal places). b. The probability that no committee member is a lawyer is approximately \(0.016\) (rounded to three decimal places).

Step by step solution

01

Identify the Total Possible Combinations

The total number of ways we can choose 5 committee members from a group of 13 (6 lawyers and 7 teachers) is given by the combination formula as \(C(13,5)\). The combination formula is defined as \[C(n,k) = n! / [k!(n-k)!]\] Where \(n\) is the total number of items to choose from, \(k\) is the number of items to choose, and \(!\) indicates factorial. Applying the formula we get the total possible combinations as 1287.
02

Calculate the Probability of All Members Being Lawyers

The number of ways we can choose 5 committee members from a group of 6 lawyers is given by the combination formula as \(C(6,5)\). Applying the formula, we get 6 combinations. The probability is then the ratio of the number of desirable outcomes to the total possible outcomes. Therefore, the probability of all members being lawyers is \(6 / 1287\).
03

Calculate the Probability of No Lawyers In The Committee

The number of ways we can choose 5 committee members from a group of 7 teachers only is given by the combination as \(C(7,5)\). Applying the formula, we get 21 combinations. Following the same method of calculating probability, the probability of no lawyers being in the committee is \(21 / 1287\).

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Most popular questions from this chapter

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. I must have made an error calculating probabilities because \(P(A \mid B)\) is not the same as \(P(B \mid A)\).

We return to our box of chocolates. There are 30 chocolates in the box, all identically shaped. Five are filled with coconut, 10 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting two caramel-filled chocolates in a row.

The local seven-digit telephone numbers in Inverness, California, have 669 as the first three digits. How many different telephone numhers are possihle in Inverness?

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A construction company is planning to bid on a building contract. The bid costs the company \(\$ 1500\). The probability that the bid is accepted is \(\frac{1}{5}\). If the bid is accepted, the company will make \(\$ 40,000\) minus the cost of the bid. Find the expected value in this situation. Describe what this value means.
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