Question

Suppose that we flip 7 fair coins - what is the probability that we have at least two tails showing?

Answer 1

X ~ Bin ( n,p)

Where n = 7 , p = 0.50 (Probability of head and tail is equally likely, that is 1/2)

Binomial probability distribution is

P(X) = ⁿC_x * p^x * ( 1 - p)^n-x

P(X >= 2) = 1 - P(X <= 1)

= 1 - [ P(X = 0) + P(X = 1) ]

= 1 - [ ⁷C₀ * 0.50⁰ * 0.50⁷ + ⁷C₁ * 0.50¹ * 0.50⁶ ]

= 1 - 0.0625

= 0.9375