Skip to main content
Puzzling

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

12
  • 1
    $\begingroup$ This answer makes the extra assumption that the events listed in the problem are independent, which wasn't stated in the question; yet the word "independent" doesn't even appear in this answer. So, you're basing your calculations on an unspoken extra assumption. $\endgroup$
    – Stef
    Commented Dec 16, 2021 at 11:19
  • $\begingroup$ When two times are given with 'equally likely' specified, doesn't that mean there are no dependencies? $\endgroup$
    – Jason Goemaat
    Commented Dec 16, 2021 at 14:05
  • 1
    $\begingroup$ No, it doesn't. Imagine the following situation: everyday the horses are fed the same menu. When horse A is fed broccoli, it runs in 50 seconds. When horse C is fed broccoli, it runs in 53 seconds. When horse A is fed lasagna, it runs in 60 seconds. When horse C is fed lasagna, it runs in 57 seconds. Now, I tell you that the probability that today's menu is broccoli is 50%, and the probability that today's menu is lasagna is 50%. Then you can safely conclude: $\endgroup$
    – Stef
    Commented Dec 16, 2021 at 14:11
  • 2
    $\begingroup$ "I think it's contrived to assume some dependency that has to itself be an equal probability for both statements to be true" I agree; it's more than just contrived, it's wrong. We can't assume anything that isn't spelled out in the problem statement. We cannot assume that the events are not independent, and we cannot assume that the events are independent. We have to solve the problem with only the information given in the problem statement. And the answer is: P(A wins) = 50%, and P(B wins or C wins) = 50%, but P(C wins) and P(B wins) cannot be calculated because we lack information. $\endgroup$
    – Stef
    Commented Dec 16, 2021 at 14:47
  • 1
    $\begingroup$ Yes, you're absolutely right. Horse C's result is completely random, with 50% chance of finishing in 53 seconds and 50% chance of finishing in 57 seconds. And we have absolutely no information about how correlated this is with Horse A's finishing times. And since we have no information, we can't just assume. Perhaps Horse C wins 25% of the time, or perhaps Horse C wins 0% of the time, or perhaps 50% of the time, or perhaps some other number. There is no way to know. $\endgroup$
    – Stef
    Commented Dec 17, 2021 at 8:06