Question

natalie can take one of her three friends with her on a trip to italy. she cant decide whom to take. nick suggests that natalie use a random number generator to assign numbers 1 through 20 to him, sarah, and mike until all the numbers are used. then natalie can pick a number from 1 to 20, and that friend will go. is nicks suggestion fair? explain.

Explanation:

For a process to be fair, each friend should have an equal probability of being selected. The total number of numbers is \(n = 20\). If we divide the \(20\) numbers among \(3\) friends, \(20\div3=\frac{20}{3}\approx6.67\). Since \(20\) is not divisible by \(3\), we cannot assign an equal number of numbers to each friend. So, the probabilities of each friend being chosen (calculated as \(\frac{\text{number of assigned numbers}}{20}\)) will not be equal.

Answer:

No, Nick's suggestion is not fair. Because \(20\) is not divisible by \(3\), each friend cannot be assigned an equal number of numbers, so their probabilities of being selected are not equal.