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If a coin is tossed an infinite number of times with a probability of getting heads each time is 0.55, what is the probability that 5 heads are observed at the 10th toss but not earlier? thanks.

 Mar 30, 2022
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If the fifth head occurs on the tenth toss, the previous nine tosses must include 4 heads and 5 tails.

 

With the probability of getting a head = 0.55, the probability of getting a tail = 0.45.

 

Thus the probability that the first nine tosses are 4 heads and 5 tails:

              9C4·(0.55)4·(0.45)5  =  0.212757,,,

 

Following this with a head requires multiplying that answer by 0.55  =  0.117016,,,

 Mar 30, 2022

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