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

Answer:

0.088

Step-by-step 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,

$P(X=x)=n C x \times p^{x} \times(1-p)^{n-x}$

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

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

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

$P(success) = \frac{50}{100} = 0.8$

x = 6

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

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

$=^{10} \mathrm{C}_{6} \times(0.8)^{6} \times(0.2)^{4}$

$=\frac{10 !}{(10-6) ! 6 !} \times(0.2621) \times(0.0016)$

$=\frac{10 \times 9 \times 8 \times 7 \times 6 !}{4 ! \times 6 !} \times 0.0004$

Solving the factorial we get,

$=\frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} \times(0.0004)$

$=\frac{5040}{24} \times 0.0004$

$=210 \times 0.0004$

P(X=6) = 0.084

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