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.(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Heads occurs 15 times out of 20 - Is it a fair coin?

**Physics Forums | Science Articles, Homework Help, Discussion**