From observations of the weather, it is known that on October 20 the probability of rain is 0.85. A certain forecast method for October 20 is correct 0.9 times if rain is predicted and 0.75 times if no rain is predicted. How much information does a real weather forecast provide 20 th of October?

From observations of the weather, it is known that on October 20 the probability of rain is 0.85. A certain forecast method for October 20 is correct 0.9 times if rain is predicted and 0.75 times if no rain is predicted. How much information does a real weather forecast provide 20 th of October?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Expert Solution

Step 1

Let us summarize the Given information:

Let us define the following Events:

R: It will rain on 20th October.

R': It will not rain on 20th October.

C: The forecast is correct.

C': The forecast is incorrect.

It is given that:

$P (R) = 0.85 P (R') = 1 - 0.85 = 0.15 P (C | R) = 0.9 P (C | R') = 0.75$

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