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 [tex]=\dfrac{P(E')}{P(E)}[/tex]
The odds against a chess-master beating a computer are 11:5. So,
[tex]\dfrac{P(E')}{P(E)}=\dfrac{11}{5}[/tex]
[tex]P(E'):P(E)=11:5[/tex]
Let P(E') and P(E) are 11x and 5x respectively.
[tex]P(E')+P(E)=1[/tex]
[tex]11x+5x=1[/tex]
[tex]16x=1[/tex]
[tex]x=\dfrac{1}{16}[/tex]
Now,
Probability the at the chessmaster will win a match against the computer P(E) is
[tex]P(E)=5\times \dfrac{1}{16}[/tex]
[tex]P(E)=\dfrac{5}{16}[/tex]
Therefore, the required probability is [tex]\dfrac{5}{16}[/tex].
