Question

We flip a fair coin 20 times. Find the probability that we obtain between 8 and 17 heads, inclusively. Show work and please explain to someone that hardly understands statistics!

Answer 1

a coin has two side,head and tail

so,P(head), p = 0.5

1-p=1-0.5

1-p=0.5

here no. of times coin flip,n = 20

applying binomial probability,

• B(x; n, P): Binomial probability - the probability that an n-trial binomial experiment results in exactly x successes, when the probability of success on an individual trial is p.
• P(X = x) =nCx*p^x*(1-p)^n-x

here,P(X = x) = 20Cx * 0.5^x * 0.5^20-x

P(8 < X < 17) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14 + P(X = 15) + P(X = 16) + P(X = 17)

                      = 20C8 * 0.5⁸ * 0.5¹² + 20C9 * 0.5⁹ * 0.5¹¹ + 20C10 * 0.5¹⁰ * 0.5¹⁰ + 20C11 * 0.5¹¹ * 0.5⁹ + 20C12 * 0.5¹² * 0.5⁸ + 20C13 * 0.5¹³ * 0.5⁷ + 20C14 * 0.5¹⁴ * 0.5⁶ + 20C15 * 0.5¹⁵ * 0.5⁵ + 20C16 * 0.5¹⁶ * 0.5⁴ + 20C17 * 0.5¹⁷ * 0.5³

                = 0.8682