Independent flips of a coin that lands on heads with

Chapter 3, Problem 59P

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QUESTION:

Problem 59P

Independent flips of a coin that lands on heads with probability p are made. What is the probability that the first four outcomes are:

H, H, H, HT, H, H, HWhat is the probability that the pattern T, H, H, H occurs before the pattern H, H, H, H?

        Hint for part (c): How can the pattern H, H, H, H occur first?

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QUESTION:

Problem 59P

Independent flips of a coin that lands on heads with probability p are made. What is the probability that the first four outcomes are:

H, H, H, HT, H, H, HWhat is the probability that the pattern T, H, H, H occurs before the pattern H, H, H, H?

        Hint for part (c): How can the pattern H, H, H, H occur first?

ANSWER:

Step 1 of 3

Let p = independent flips of a coin that lands head.

1 - p =  independent flips of a coin that lands Tail.

a) The claim is to find the probability that the first four outcomes are H, H, H, H.

Then, P(H, H, H, H) = (p) (p) (p) (p)

                          =

Hence, the probability that the first four outcomes are H, H, H, H, is .

 

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