Question

You and your friend are playing a game where you spin a circular spinner with nine numbered sections of equal size. In this game, you win if the spinner lands on 1,4, or 7. Your friend wins if the spinner lands on 2,5, or 8. You tie if the spinner lands on 3,6, or 9.

All the possible outcomes of the game are listed in the sample space


S= { 1,2,3,4,5,6,7,8,9}


If we take A= { 1,3,4,6,7,9} as a subset of the sample space, which of the statements below describe the subset A?


a) The subset consists of all the outcomes where your friend loses or there is a tie.

b) The subset consists of all the outcomes where your friend ties.

c) The subset consists of all the outcomes where there is not a tie and your friend does not win.

d) The subset consists of all the outcomes where you do not lose.

Answer 1

a) The subset consists of all the outcomes where your friend loses or there is a tie.

d) The subset consists of all the outcomes where you do not lose.

Both are correct.

Explanation:

The subset A= { 1,3,4,6,7,9} removes 2,5 and 8 from the sample space of the game. Those three numbers are the ones for which your friend wins, therefore, the subset consists of all outcomes for which you either win (your friend loses) or there is a tie.

Checking the given alternatives, there are actually two correct ones. Alternatives a) and d) describe the same sample space (you not losing = your friend not winning).

Therefore, the two possible answers are:

a) The subset consists of all the outcomes where your friend loses or there is a tie.

d) The subset consists of all the outcomes where you do not lose.