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Asked Sep 17, 2019
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A fair coin is flipped six times. What is the probability that tails occurs exactly 6 times if it is known that tails occurs at least four times?
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A fair coin is flipped six times. What is the probability that tails occurs exactly 6 times if it is known that tails occurs at least four times?

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Expert Answer

Step 1

Conditional rule:

The formula for probability of A given B is,

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P(Aand B) P(AB)PAand B) P(B)

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Step 2

In a coin tossing, the probability of getting a head and a tail is equal and the corresponding probability of each is equal to ½. Here,  the coin is tossed 6 times. Thus, it follows a binomial distribution with n=6 and p=1/2. That is,

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6-x P(Xx) ,x 0,1,2,3,4,5,6 х

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Step 3

Finding the probability that tails occurs exactly 6 times if it is known that tails occurs at least four times:

The prob...

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*-0-CH(4*| 6 6-6 6 P(X 6) 6 2 0.0156

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