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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.
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
A mammogram can typically identify correctly 85% of cancer cases
This means that
Probability of a positive test.
85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So
What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer