Infer posterior after losing pick
Problem Description
You are observing a jumping contest involving three cats:
- Cat 1 (most athletic) wins with probability
p1. - Cat 2 (middle athletic) wins with probability
p2. - Cat 3 (least athletic) wins with probability
p3.
It is given that p1 + p2 + p3 = 1.
Before the contest begins, you randomly select one cat to cheer for. Each cat has an equal probability (1/3) of being chosen.
After the contest concludes, you learn that the cat you chose did not win. Assume your choice of cat does not influence the outcome of the contest.
Question
Given this information, what is the probability that you had initially picked the most athletic cat (Cat 1)?
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Core dilemma
Correctly applying conditional probability and Bayes' Theorem to update beliefs based on observed evidence in a multi-event scenario.
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Infer posterior after losing pick
Problem Description
You are observing a jumping contest involving three cats:
- Cat 1 (most athletic) wins with probability
p1. - Cat 2 (middle athletic) wins with probability
p2. - Cat 3 (least athletic) wins with probability
p3.
It is given that p1 + p2 + p3 = 1.
Before the contest begins, you randomly select one cat to cheer for. Each cat has an equal probability (1/3) of being chosen.
After the contest concludes, you learn that the cat you chose did not win. Assume your choice of cat does not influence the outcome of the contest.
Question
Given this information, what is the probability that you had initially picked the most athletic cat (Cat 1)?