Question

A surgical technique is performed on 10 patients. You are told there is an 80% chance of success. Find the probability that the surgery is successful for exactly 6 patients.

Answer 1

0.0881

Explanation:

This is binomial distribution probability that can be solve using the formula:

`P(x)=(n!)/((n-x)!x!)p^(x)q^(n-x)`

Where n is total number of trials [here it is 10]

x is what we want to find [here, we want for 6 patients, so x = 6]

p is probability of success [p = 0.8]

q is probability of failure [ 1 - p = q = 0.2]

Substituting, we get:

`P(x)=(n!)/((n-x)!x!)p^(x)q^(n-x)\\P(x=6)=(10!)/((10-6)!6!)(0.8)^(6)(0.2)^(5)\\P(x=6)=0.0881`