Question

A surgical technique is performed on seven patients. You are told that there is a 80% chance of success. Let X be a random variable that showing the number of successes with a binomial distribution. Find the probability that the surgery is successful for exactly five patients? Hint: The variable X has a binomial distribution. a) 0.768 b) 0.275 c) 0.423 d) 0.327

Answer 1

The probability that the surgery is successful for exactly five patients is 0.275, so the correct option is b.

Step-by-step explanation:

To find the probability that the surgery is successful for exactly five patients, we can use the binomial probability formula.

In this case, X follows a binomial distribution with parameters n=7 (total number of patients) and p=0.8 (probability of success).

The probability mass function for X is given by P(X=k) = (n C k) * (p^k) * ((1-p)^(n-k)), where (n C k) represents the number of combinations of n items taken k at a time.

Substituting the values, we have P(X=5) = (7 C 5) * (0.8^5) * (0.2^2) = 0.2753472.

Therefore, the probability that the surgery is successful for exactly five patients is 0.275, giving the correct option as b.