Question

What is the probability of randomly selecting the committee members and getting the youngest of the qualified candidates?

Answer 1

The probability of randomly selecting the youngest of the qualified candidates depends on the total number of qualified candidates and the number of committee members to be selected.

Step-by-step explanation:

To calculate the probability, we need the total number of qualified candidates and the number of committee members to be selected. Let's denote the total number of qualified candidates as N and the number of committee members to be selected as k.

The probability of randomly selecting the youngest candidate is determined by the number of ways to choose the youngest candidate out of the total candidates. Assuming all candidates are equally likely to be selected, the probability (P) can be calculated using the formula:

`\[ P = (1)/(N) \]`

This is because there is only one youngest candidate, and the total number of candidates is N.

If the committee is selecting more than one member, the probability would be calculated differently. For example, if the committee is selecting a group of k members, and the youngest candidate needs to be part of this group, the probability becomes:

`\[ P = (1)/(N) * (1)/(N-1) * \ldots * (1)/(N-k+1) \]`

This formula accounts for the decreasing number of candidates available for selection after each member is chosen.

Understanding probability in the context of committee selection is essential for making informed decisions and evaluating the likelihood of specific outcomes based on the available choices.