Three horses, call them A, B, and C, are going to race against each other. The probability that A will win the race is 1⁄3 and the probability that B will win the race is 1⁄4 . What is the probability that C will win the race?

Question

Three horses, call them A, B, and C, are going to race against each other.  The probability that A will win the race is  1⁄3  and the probability that B will win the race is  1⁄4 .  What is the probability that C will win the race?

anonymous · Answer

Law to total probability:  The sum of the probabilities of each outcome adds up to 1.

So  1/3 + 1/4 + pobability C wins = 1

anonymous · Answer

P(C) = 1 - P(A) - P(B) = 5/12