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Question

How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?


Solution

Let the required number of trials be n

Probablity of getting a head, p=12
Probability of getting a tail, q=12

According to the question:

P (at least one head) >80%

P(x1)>810

1P(x<1)>810

P(x=0)<1810

 nC0 qn p0<210

1×(12)n <210

(12)n <15 or 0.2

(12)n=18,116,132,...

n=3, 4, 5,... will satisfy

Hence, n3

Mathematics

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