At the racetrack, you as a better are hoping to win big by betting on one of the

Question

At the racetrack, you as a better are hoping to win big by betting on one of the either horses running that day. You know nothing about horse racing so you have a prior probability of any horse winning the race to be one in eight (1/8). However, to improve your odds you listen to those placing bets, and you also are able to do some sleuthing and discover the track records of those betters. You discover that when the crowd of betters favors a horse, it wins 6096 of the time, and when the crowd doesn't favor a horse it wins 596 of the time (the rest of the cases the crowd doesn't have a favorite). Suppose then a horse named Ser Speedy is the favorite to win. Based on this information about the track record of the betters, what would be your guess as to the probability (as a percentage) of Ser Speedy winning?

Explanation / Answer

This is the case of conditional probability, i.e. the probability of horse winning given when the horse is favourite.

P(A) = Probability of horse winning

P(B) = Horse is favourite.

P(A/B) = Probabilty of horse winning given it is the favourite = 60%

Let me know if the answer is different. As far as I know there is no other answer.

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