Question

Recent news articles have discussed the connection between a rare genetic mutation and breast cancer in women. One of the companies offering this BRCA genetic test is Quest, and this company claims a 97.5% accuracy rate. In the general population about 1 in 390 people would actually carry this BRCA1 genetic mutation. Hint: Construct a table as in your course materials. Use a population size of 39000 women. What is the likelihood that someone does not have the BRCA mutations, if they test positive? (Round your probability to the nearest tenth of a percent!) Probability = %

Answer 1

Here Acccuracy rate of test = 97.5% = 0.975

Pr(Carrying BRCA1 genetic mutation) = 1/390

Here total population = 39000

So expected women to have BRCA1 mutation = 39000 * 1/390 = 100

Expected number of women who is not affected = 39000 - 100 = 38900

No test is 97.5% accurate that means

it will test positive 97.5% when there is mutation and test negative 97.5% when there is no mutation.

so expected women to have positive result when postive mutated = 100 * 0.975 = 97.5

expected women to have negative result when negatively mutated = (39000 - 100) * 0.975 = 37927.5

		Test Results
		Yes	NO	Total
Mutation	Yes	97.5	2.5	100
	NO	972.5	37927.5	38900
	Total	1070	37930	39000

Here

Pr(Test positive when she doesnot have the BRCA mutations) = 972.5/1070 * 100 = 90.9%