If the odds against deborah's winning first prize in a chess tournament are 2 to 7, what is the probability of the event that she will win first prize? (type an integer or a fraction.)

Probability of winning the prize will be 0.222

Step-by-step explanation:

Odd against Deborah's winning the first prize are 2 to 7

Means ratio of unfavorable outcomes to favorable outcomes

Total number of outcomes = 2+7 =9

We have top find the probability of winning the first prize

So probability

Probability of winning first prize by Deborah is,

In the question,

The odds against the Deborah's winning the first prize in the chess tournament is given by the fraction or the possibility,

Now,

We need to find out the probability of an event in which she wins the first prize.

Now,

We are given the probability of losing of Deborah's first prize is,

So,

The probability of getting the first prize = 1 - Probability of not winning first prize

So,

Therefore, the probability of winning first prize by Deborah is,