You have two biased coins. Coin A comes up heads with probability 0.6. Coin B comes up heads with probability 0.3. However, you are not sure which is which so you choose a coin randomly and you flip it. If the flip is heads, you guess that the flipped coin is A; otherwise, you guess that the flipped coin is B. Let events A and B designate which coin was picked. What is the probability P[C] that your guess is correct?

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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You have two biased coins. Coin A comes up heads with probability 0.6. Coin B comes up heads with probability 0.3. However, you are not sure which is which so you choose a coin randomly and you flip it. If the flip is heads, you guess that the flipped coin is A; otherwise, you guess that the flipped coin is B. Let events A and B designate which coin was picked. What is
the probability P[C] that your guess is correct?

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