Question

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.)

Answer 1

Probability of winning first prize by Deborah is,

`(5)/(7)\\`

Explanation:

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,

`Probability=(2)/(7)`

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,

`(2)/(7)`

So,

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

So,

`Probability\,of\,getting\,the\,first\,prize=1-(2)/(7)=(5)/(7)\\Probability\,of\,getting\,the\,first\,prize=(5)/(7)\\`

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

`(5)/(7)\\`

Answer 2

Probability of winning the prize will be 0.222

Explanation:

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

Means ratio of unfavorable outcomes to favorable outcomes
`=(2)/(7)`

Total number of outcomes = 2+7 =9

We have top find the probability of winning the first prize

So probability
`=(number\ of\ favorable\ outcomes)/(total\ outcomes)=(2)/(9)=0.222`