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ElenaW [278]
3 years ago
9

The National Cancer Institute estimates that 3.65% of women in their 60s get breast cancer. A mammogram can typically identify c

orrectly 85% of cancer cases and 95% of cases without cancer. What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
Mathematics
1 answer:
masha68 [24]3 years ago
7 0

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.

P(B|A) = \frac{P(B)*P(A|B)}{P(A)}

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 P(B) = 0.0365

A mammogram can typically identify correctly 85% of cancer cases

This means that P(A|B) = 0.85

Probability of a positive test.

85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So

P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792

What is the probability that a woman in her 60s who has a positive test actually has breast cancer?

P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

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