2. The probability that a particular screening test for breast cancer will be po

Question

2. The probability that a particular screening test for breast cancer will be positive when, in fact, the patient does, in fact, have breast cancer is 0.9. You may assume that the outcome of any one test is independent of the outcome of any other. One morning five women, each of whom does have breast cancer, take the test. What is the probability that:

(a) All five of the tests are positive?

(b) The first test is negative and the others positive?

(c) at least one of the five tests is negative?

Explanation / Answer

p=0.9

(a) Required probability = p^5 = 0.59049

(b) Required probability = (1-p)*p^4 = 0.06561

(c) Required probability = 1- P(No test in negative) = 1-P(All tests are positive) = 1-0.59049 = 0.40951

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