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phono

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I have to answer this question by using references to expectation and probability as well as any other relevant considerations. My textbook says that 96% of the time, the number of heads in 20 flips will be between 6 and 14 inclusive. Prove this.

Ok I can prove the answer in the textbook using Binomial Theorem.

Probability of k heads from n flips of a fair coin is n choose k = n!/((n - k)! k!) divided by total possibiliries = 2^n

Sp P(5) heads = (20 choose 5)/1048576

Sum P(n) from n = 6 to 14

(38760 + 77520 + 125970 + 167960 + 184756 + 167960 + 125970 + 77520 + 38760)/1048576

= 1005176/1048576 ~ 0.9586 ~ 96%

Edit: The question actually says "do you think the coin is fair?", sorry. Using references to expectation as well.

Thanks

Ok I can prove the answer in the textbook using Binomial Theorem.

Probability of k heads from n flips of a fair coin is n choose k = n!/((n - k)! k!) divided by total possibiliries = 2^n

Sp P(5) heads = (20 choose 5)/1048576

Sum P(n) from n = 6 to 14

(38760 + 77520 + 125970 + 167960 + 184756 + 167960 + 125970 + 77520 + 38760)/1048576

= 1005176/1048576 ~ 0.9586 ~ 96%

Edit: The question actually says "do you think the coin is fair?", sorry. Using references to expectation as well.

Thanks

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