Question

Situation A:John and Martin are players on their school baseball team. During a tournament, their team captain, Robert, suggests flipping a coin to decide who will bat first. If the coin lands heads up, then John bats first. If it lands tails up, then Martin bats first.Situation B:A group of friends plan their weekend activities based on the rolled result of a die. If the rolled result of the die is 1, 3, or 5, then they will go out for dinner. If the rolled result of the die is 2, 4, or 6, then they will order pizza and rent a movie.Part ADetermine whether the two situations are statistically fair or not. Explain your answer.

Answer 1

To answer this question, we have two situations in which we have two events that are used to decide a situation. In each case, we need to determine if the outcomes are equally likely.

Then we can proceed as follows:

First Situation

We have John and Martin, and it is about to decide who will be to bat first.

If we flip a coin to decide that, we know, from probability theory, that the probability to get a head is 0.50, and the probability of getting a tail is also 0.50. Therefore, this situation is statistically fair.

Second Situation

The results of a die are equally likely (if we have a fair die), and the outcomes are 1, 2, 3, 4, 5, and 6.

Then if we calculate the probability of having 1, 3, and 5, we have:

`P(1,3,5)=(3)/(6)=(1)/(2)`

And if we calculate the probability of getting 2, 4, or 6 is also:

`P(2,4,6)=(1)/(6)+(1)/(6)+(1)/(6)=(3)/(6)=(1)/(2)`

Then both events are equally likely to happen.

Therefore, in summary, we can say that the two situations are statistically fair.