# Answer to Question #16494 in Statistics and Probability for selena

Question #16494

Three swimmers in 100m race, swimmer A is twice as likely to win as B and three times as to win as C. Find the probability that B or C wins. show us workings

Expert's answer

Let us assume that probability that A wins is P.

Then probability that B wins is P/2

And probability that C wins is& P/3

We know that someone should win, that is why sum of all probabilities should be 1

P+P/2+P/3=1

6P+3P+2P=6

11P=6

P=54.5%

Probability that B wins is 54.5%/2=27.3%

Probability that C wins is 54.5%/3=18.2%

Then probability that B wins is P/2

And probability that C wins is& P/3

We know that someone should win, that is why sum of all probabilities should be 1

P+P/2+P/3=1

6P+3P+2P=6

11P=6

P=54.5%

Probability that B wins is 54.5%/2=27.3%

Probability that C wins is 54.5%/3=18.2%

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