A track star runs two races on a certain day.

Question

A track star runs two races on a certain day. The probability that he wins the first race is 0.7; the probability that he wins the second race is 0.6. Also whether or not he wins one race is independent of whether or not he wins the other race. Find the probability that (a) he wins at least one race. [4] (b) he wins exactly one race. [3] (c) he wins neither race. [3]

Answer 1

Possible outcomes are win 2 , lose 2 or win 1and lose 1

P( wins first race) = .7 then P( loses first race)= .3

P(wins second race ) =.6 then P(loses second race) = .4

I will answer the part c first. P( loses both races)= .3 x .4 = .12

Part a P he wins at least 1 race would be all other outcomes = 1.00 -.12 = .88

To win just one race he could either win the first and lose the second ( .7 x .4 = .28) or lose the first and win the second ( .3 x .6 = .18 ) which totals to .28 +.18 = .46