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Statistics / A First Course in Probability 9 / Chapter 3 / Problem 8STE

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

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Chapter 3, Problem 8STE

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QUESTION:

Problem 8STE

Show that

Suppose that, before new evidence is observed, the hypothesis H is three times as likely to be true as is the hypothesis G. If the new evidence is twice as likely when G is true than it is when His true, which hypothesis is more likely after the evidence has been observed?

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QUESTION:

Problem 8STE

Show that

Suppose that, before new evidence is observed, the hypothesis H is three times as likely to be true as is the hypothesis G. If the new evidence is twice as likely when G is true than it is when His true, which hypothesis is more likely after the evidence has been observed?

ANSWER:

Step 1 of 2

We have to show that $\frac{P(H/E)}{P(G/E)}=\frac{P(H)\ P(E/H)}{P(G)\ P(E/G)}$

Now by using the bayes theorem $P(H/E)=\frac{P(H)\ P(E/H)}{P(E)}$

$P(G/E)=\frac{P(G)\ P(E/G)}{P(E)}$

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