Respuesta :
Answer:
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test.
Event B: Having breast cancer.
3.65% of women in their 60s get breast cancer
This means that [tex]P(B) = 0.0365[/tex]
A mammogram can typically identify correctly 85% of cancer cases
This means that [tex]P(A|B) = 0.85[/tex]
Probability of a positive test.
85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So
[tex]P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792[/tex]
What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
[tex]P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917[/tex]
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer
