Infer posterior after losing pick

Q: Infer posterior after losing pick

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Question

Conditional probability after observing a loss

You have three cats in a jumping contest:

Cat 1 (most athletic) wins with probability p1
Cat 2 (middle) wins with probability p2
Cat 3 (least athletic) wins with probability p3

with p1 + p2 + p3 = 1.

You pick a cat uniformly at random (each with probability 1/3) to cheer for before the contest. After the contest, you learn that your chosen cat did not win.

Assuming your choice does not influence the outcome, what is the probability that you had picked the most athletic cat?

Infer posterior after losing pick

Conditional probability after observing a loss

Solution

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