Question

Spinner goes 1-4. Jose spins the spinner 8 times. In those 8 spins, the arrow never lands on 3. Based on this information, should Jose be concerned that the spinner is unfair? Explain.

Answer 1

If the spinner was fair, the probability of landing on 3 in a single spin is 1/4. The probability of never landing on 3 in 8 spins is (3/4)^8 = 0.1. The probability of landing on 3 at least once in 8 spins is 1 - 0.1 = 0.9.
Therefore Jose should be concerned that the spinner is unfair.

Answer 2

Well this is a more complicated question than it may seem. The laws of probability are based on observations whose number is very large or actually as the number of observations approaches infinity. So on the one hand, you should be concerned that you get 0/8 to land on 3. However, 42/500 land on 3 so your ratio has improved. It's not near 125 but it's also not 0. If it remained at 0, you would begin to be concerned and rightly so. Perhaps if you did 5000, you would be less concerned as the ratio improved and got closer to 1/4 of the observations. So at this point I don't think you have enough information to determine that the spinner is unfair.