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.

Group of answer choices

0.088

0.0328

0.1208

Answer 1

0.088

Explanation:

Answer 2

Option A

ANSWER:

The probability that the surgery is successful for exactly 6 patients is 0.088

SOLUTION:

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

For binomial distribution, the probability mass function for random variable X is given as,

`P(X=x)=n C x * p^(x) *(1-p)^(n-x)`

Given, that the total number of patients is n=10

The chance of success for surgical technique is p=80%.

`\text { Probability of getting success p(success) }=\frac{\text {no of favourable outcomes}}{\text {total possible outcomes}}`

`P(success) = (50)/(100) = 0.8`

x = 6

The probability for surgery is successful for exactly 6 patients is given by

`\mathrm{P}(\mathrm{X}=6) = ^(10) \mathrm{C}_(6) *(0.8)^(6) *(1-0.8)^(10-6)`

`=^(10) \mathrm{C}_(6) *(0.8)^(6) *(0.2)^(4)`

`=(10 !)/((10-6) ! 6 !) *(0.2621) *(0.0016)`

`=(10 * 9 * 8 * 7 * 6 !)/(4 ! * 6 !) * 0.0004`

Solving the factorial we get,

`=(10 * 9 * 8 * 7)/(4 * 3 * 2 * 1) *(0.0004)`

`=(5040)/(24) * 0.0004`

`=210 * 0.0004`

P(X=6) = 0.084

Answer is near to option A. Hence probability that the surgery is successful for exactly 6 patients 0.088.