A softball player bats twice in a game. Each at-bat results in an out (O), getting on base (B), or hitting a home run (H). List every possible outcome in set notation.

Answer 1

{BB, BO, BH, OO, OB, OH, HH, HO, HB} (A total of 9 possibilities where, for example, BH means that the batter got a base hit on the first at bat and got a home run on the second)

Answer 2

Hi Janson,

This is just a straight application of set notation.

A player bats twice, so each result must be of the form (x, y) where x = result for at-bat #1 and y = result for at-bat #2. Also, both x and y are taken from the set {O, B, H}

Therefore, every possible outcome, in set builder notation, is { (x, y) | x, y ∈ {O, B, H} }

Since there are 3 possible values for x and 3 for y, this outcome set must contain 3 x 3 = 9 values, ranging from (O, O) to (H, H).