Answer:
31.77% probability the surgery is successful for exactly five patients.
Step-by-step explanation:
For each patient, there are only two possible outcomes. Either the surgery is successful, or it is not. The probability of the surgery being successful for a patient is independent of other patients. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
A surgical technique is performed on seven patients.
This means that
You are told there is a 70% chance of success.
This means that
Find the probability the surgery is successful for exactly five patients.
This is P(X = 5).
31.77% probability the surgery is successful for exactly five patients.