The 2016 Kentucky Derby had (20) horses participate in the Run for the Roses, an
ID: 3207609 • Letter: T
Question
The 2016 Kentucky Derby had (20) horses participate in the Run for the Roses, and the 2015 Kentucky Oaks had (14) horses participate. A first time viewer was interested in placing a wager on these two races. What is the probability of this first timer picking the winner of the Kentucky Derby and the Kentucky Oaks at the same time? After some thought, this person figured out they could pick the Exacta (picking the 1st and 2nd place finishers) or Trifecta (picking the 1st, 2nd and 3rd place horses) and receive a larger payout. What is the probability that this person will correctly pick the Exacta in the Oaks or the Trifecta in the Derby?
Explanation / Answer
Answer:
Total number of horses in Kentucky Derby = 20
Probability of picking winning horse in Kentucky Derby = 1 winner out of 20 = 1/20
Total number of horses in Kentucky Oaks = 14
Probability of picking winning horse in Kentucky Oaks = 1 winner out of 14 = 1/14
Since these two are independent events therefore probability of winning both Derby at the same time = P(A and B) = P(A)*P(B) = (1/20)*(1/14) = 1/280 =0.00357
Probability of Picking Exacta in the Oaks (that means picking top two finishers in order):
number of possibilities = (number of ways 1st horse can win from 14horses)*(number of ways 2nd horse can win from remaining 13 horses) = 14*13
Therefore probability of Exacta = 1/(14*13) = 1/182 = 0.005495
Probability of Picking Trifecta in the Derby (that means picking top three finishers in order):
number of possibilities = (number of ways 1st horse can win from 20horses)*(number of ways 2nd horse can win from remaining 19 horses)*(number of ways 3rd horse can win from remaining 18horses)* = 20*19*18
Therefore probability of Trifecta = 1/(20*19*18) = 1/6840 = 0.000146
Probability of picking Exacta in Oaks or Trifecta in Derby P(A or B) = P(A) + P(B) = 1/182 + 1/6840 = 7022/1244880 = 0.005461
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