Mathematics: The odds against a chess-master beating a computer are 11:5. What is the probability the at the chessmaster will win a match against the chessmaster?

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The odds against a chess-master beating a computer

alexsandra120505

06.02.2022

Given:

The odds against a chess-master beating a computer are 11:5.

To find:

The probability the at the chessmaster will win a match against the computer?

Solution:

Let E be the event the chessmaster will win a match against the computer.

Odds against a chess-master beating a computer $=\dfrac{P(E')}{P(E)}$

The odds against a chess-master beating a computer are 11:5. So,

$\dfrac{P(E')}{P(E)}=\dfrac{11}{5}$

P(E'):P(E)=11:5

Let P(E') and P(E) are 11x and 5x respectively.

P(E')+P(E)=1

11x+5x=1

16x=1

$x=\dfrac{1}{16}$

Now,

Probability the at the chessmaster will win a match against the computer P(E) is

$P(E)=5\times \dfrac{1}{16}$

$P(E)=\dfrac{5}{16}$

Therefore, the required probability is $\dfrac{5}{16}$ .

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