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Two coins fall "heads up" with probabilities w1 and w2 respectively. Both coins are tossed. What...

Two coins fall "heads up" with probabilities w1 and w2 respectively. Both coins are tossed. What is the probability that they show the same face? If they do show the same face, what is the probability that theface they both show is "heads"?

Math   Statistics-And-Probability   
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Answer #1

Solution:

According to the provided information,

There is two coin fall "heads up" with probabilities w1 and w2 respectively.

Since a coin has two faces and if the probability of getting "heads up" is w then the probability of getting another side is 1-w

The probability that they show the same face can be calculated as:

And,

The probability that the face they both show is "heads" can be calculated as:

Therefore, the probability that the face they both show is "heads" is w1w2

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