Respuesta :
Answer:
0.0049 = 0.49% probability that she actually has breast cancer
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test result
Event B: Breast cancer
Probability of a positive test result:
4% of (1 - 0.0002)
98% of 0.0002
So
[tex]P(A) = 0.04*(1 - 0.0002) + 0.98*0.0002 = 0.040188[/tex]
Having breast cancer and testing positive.
98% of 0.0002
So
[tex]P(A \cap B) = 0.98*0.0002 = 0.000196[/tex]
What is the probability that she actually has breast cancer?
[tex]P(B|A) = \frac{0.000196}{0.040188} = 0.0049[/tex]
0.0049 = 0.49% probability that she actually has breast cancer
