Question

14-7. Ann, Jim, John, and Nancy are scheduled to compete in a racquetball tournament. An is twice as likely to beat Jim, and Jim is at the same level as John. Nancy's past winning record against John is one out of three. Determine the following (a) The probability that Jim will win the tournament. (b) The probability that a woman will win the tournament. (c) The probability that no woman will win.

Answer 1

let probability that Ann will win =a
therefore probability Jim will win =a/2 =probability John will win

and probability of Nancy will win =(a/2)/2=a/4

since all above events are mutually exclusive and collectively exhaustive

sum of all probabilities is 1

a+a/2+a/2+a/4 =1

a*(9/4) =1

a =4/9

a)

probability Jim will win =(4/9)/2 =2/9

b)P(women will win) =P(Ann will win )+P(Nancy will win) =(4/9)+(4/9)/4 =5/9

c) P(no women will win) =1-P(women will win) =1-5/9 =4/9