Question

A new surgery is successful 85% of the time. If the results of 7 such surgeries are randomly sampled, what is the probability that at least 6 of them are successful? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.

Answer 1

X ~ Bin ( n , p )

Where n = 7 , p = 0.85

Binomial probability distribution is

P(X) = ⁿC_x p^x ( 1- p)^n-x

So,

P(X >= 6) = P(X = 6) + P(X = 7)

= ⁷C₆ * 0.85⁶ * (1 - 0.85) + ⁷C₇ * 0.85⁷ * (1 - 0.85)⁰

= 0.72