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Chapter 11: Problem 42

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 Democrats.

Short Answer

Expert verified
The probability of selecting no Democrats is approximately 0.429

Step by step solution

01

Calculate Total Number of Possible Outcomes

Firstly, calculate the total number of ways 2 people can be selected from a group of 15. This can be calculated as \({15 \choose 2}\), which equals 105.
02

Calculate Outcomes of Selecting non-Democrats

Next, calculate the total number of ways 2 people that are not Democrats can be selected. This group consists of 6 Republicans and 4 Independents, which equals 10 people. The total number of ways 2 people can be chosen from this group is \({10 \choose 2}\), which equals 45.
03

Calculate the Probability

Finally, the probability of the required event can be calculated as the ratio of number of ways of selecting 2 non-Democrats to the total number of possible outcomes. This is \({10 \choose 2}\) / \({15 \choose 2}\), which simplifies to 45 / 105, and further simplifies to 0.429.

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Most popular questions from this chapter

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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