How many out of twelve?

If you are three times as likely to lose as you are to win, then how many games should you expect to win out of 12 games?

(on each game you must either win or lose.)

4 6 3 2

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2 solutions

Ram Mohith
Apr 30, 2018

The statement "If you are three times as likely to lose as you are to win" means that for every one match we win we are losing three matches . That is If we play 4 matches we will lose 3 of them . So probability of winning = 1 4 \large\frac{1}{4}

Let us say we won x x matches out of 12 .

So, x 12 = 1 4 \large\frac{x}{12} = \frac{1}{4}

x = 12 4 = 3 \implies x = \large\frac{12}{4} = 3

Therefore , we must win 3 matches \color{#20A900}\boxed{\text{3 matches}} to satisfy the given equation .

Mike Pannekoek
Apr 29, 2018

The total amount of games you win and lose must add up to twelve. If you add 3 times amount of games that you expect to win (which should be the expected number of games you lose) to the amount of games you expect to win, you should get the 12 total games. Thus 4 times the amount of games that you expect to win is 12, which means that you should expect to win 3 games total.

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