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Chapter 5: Q. 103. (page 337)

An athlete suspected of using steroids is given two tests that operate independently of each other. Test A has probability 0.9of being positive if steroids have been used. Test B has probability 0.8of being positive if steroids have been used. What is the probability that neither test is positive if the athlete has used steroids?

a. 0.08

b. 0.28

c. 0.02

d. 0.38

e. 0.72

Short Answer

Expert verified

The required answer is:

The correct option is(c)0.02

Step by step solution

01

Given information

The Test Ahas the probability 0.9of being positive if steroids have been used. The Test Bhas the probability 0.8of being positive if steroids have been used.

02

Calculation

Let Adenote the event that an athlete is given a test A.
Let Bdenote the event that an athlete is given a test role="math" localid="1654796054098" B.

P(A)=0.9,P(B)=0.8

PAa^<B'=PA'PB'(as A and B are independent)

1-P(A)1-P(B)=(1-0.9)(1-0.8)=0.1(0.2)=0.02

Therefore the correct option is(c)

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