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Statistics / A First Course in Probability 9 / Chapter 3 / Problem 29TE

A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross

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In Laplace’s rule of succession (Example 5e), show that if

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QUESTION:

Problem 29TE

In Laplace’s rule of succession (Example 5e), show that if the first nflips all result in heads, then the conditional probability that the next mflips also result in all heads is (n + 1)/(n + m + 1).

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QUESTION:

Problem 29TE

In Laplace’s rule of succession (Example 5e), show that if the first nflips all result in heads, then the conditional probability that the next mflips also result in all heads is (n + 1)/(n + m + 1).

ANSWER:

Step 1 of 2

(a)

In Laplace’s rule of succession (Example 5e), show that if the first $n$ flips all result in heads, then the conditional probability that the next $m$ flips also result in all heads is

$\frac{(n+1)}{(n+m+1)}$

We can write the conditional probability that the next $m$ flips also result in all heads as,

$P(next\ m\ heads\ |\ first\ n\ heads)=\frac{P(first\ n+m\ are\ heads)}{P(first\ n\ heads)}$

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