Respuesta :
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A surgical technique is performed on seven patients.
This means that [tex]n = 7[/tex]
You are told there is a 70% chance of success.
This means that [tex]p = 0.7[/tex]
Find the probability the surgery is successful for exactly five patients.
This is P(X = 5).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{7,5}.(0.7)^{5}.(0.3)^{2} = 0.3177[/tex]
31.77% probability the surgery is successful for exactly five patients.
