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# Probability Questions on Funds, Elections, Pollution and Cars

1. The board of directors for the ABC investment Fund has 10 members. If 3 members of randomly selected to oversee the auditors, the probability that the 3 wealthiest members are selected is 1/120. Is this correct???

2. In problem #1, if members are elected to the positions of chairperson, vice chairperson, and treasurer how many different slates are possible?

3. The EPA used a tailpipe test to determine which of 116,667 cars generated too much pollution. It is estimated that 1% of cars fail such a test. If 20 20 cars are randomly selected from the group of 116,667, How many are expected to fail the tailpipe test?

4. In problem #3, if two different cars are randomly selected , the probability that they both fail the tailpipe test is 0.0001. Is this true?

#### Solution Preview

1. The board of directors for the ABC investment Fund has 10 members. If 3 members of randomly selected to oversee the auditors, the probability that the 3 wealthiest members are selected is 1/120. Is this correct???

We know the board of directors has 10 members. Let's call them A, B, C, D, E, F, G, H, I, and J. Say that members A, B, and C are the 3 wealthiest. So, now the problem becomes: what is the probability of selecting members A, B, and C?

The probability that we pick one of those three is 3/10. Then, there are 2 left to choose out of a group of 9. The probability of ...

#### Solution Summary

This problem set consists of four questions that involve calculating probabilities (questions 1, 3, and 4) and calculating the number of combinations (question 2). The solution provides complete answers and explanations for each of the four questions.

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