Respuesta :
Answer:
[tex]P(X = 1) = 0.1470[/tex]
Step-by-step explanation:
There can only be two outcomes. Either a woman has breast or ovarian cancer, or she hasn't. So we can solve this problem by the binomial probability formula.
Binomial probability
Th 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 combinatios 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.
In this problem
We want to find P(X = 1), so [tex]x = 1[/tex].
There are 5 woman, so [tex]n = 5[/tex]
There is a 51% probability that a woman with this gene has cancer, so [tex]p = 0.51[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{5,1}.(0.51)^{1}.(0.49)^{4} = 0.1470[/tex]
