There are K + 1 coins in a box. When flipped, the ith coin will turn up heads with the probabilityi 0,1,..,k. A coin is randomly selected from the box and is then repeatedly flipped. If the first n flips all result in heads, what is the conditional probability that the (n + 1)st flip will do likewise?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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(The Laplace's rule of succession)
There are K+1 coins in a box. When flipped, the ith coin will turn up heads with the probability, i = 0,1,.., k.
A coin is randomly selected from the box and is then repeatedly flipped. If the first n flips all result in heads,
what is the conditional probability that the (n + 1)st flip will do likewise?
Transcribed Image Text:(The Laplace's rule of succession) There are K+1 coins in a box. When flipped, the ith coin will turn up heads with the probability, i = 0,1,.., k. A coin is randomly selected from the box and is then repeatedly flipped. If the first n flips all result in heads, what is the conditional probability that the (n + 1)st flip will do likewise?
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