Question

If the odds against​ Deborah's winning first prize in a chess tournament are 1 to 7, what is the probability of the event that she will win first​ prize?

Answer 1

7/8

Explanation:

Odds against are the ratio between losses and wins.

odds against = L / W

Probability of winning is the ratio between wins and all games.

probability = W / games

probability = W / (W + L)

The odds against are 1 to 7.

1/7 = L / W

W = 7 L

The probability is therefore:

P = (7 L) / (7 L + L)

P = 7/8