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Answers without the blur. Sign up and see all textbooks for free! Q. 103.

Expert-verified Found in: Page 337 ### The Practice of Statistics for AP Examination

Book edition 6th
Author(s) Daren Starnes, Josh Tabor
Pages 837 pages
ISBN 9781319113339 # An athlete suspected of using steroids is given two tests that operate independently of each other. Test A has probability $0.9$of being positive if steroids have been used. Test B has probability $0.8$of 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. $0.72$

The correct option is $\left(c\right)0.02$

See the step by step solution

## Step 1: Given information

The Test $A$has the probability $0.9$of being positive if steroids have been used. The Test $B$has the probability $0.8$of being positive if steroids have been used.

## Step 2: Calculation

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

$P\left(A\right)=0.9,P\left(B\right)=0.8$

$P\left(A\stackrel{^}{a}<{B}^{\text{'}}\right)=P\left({A}^{\text{'}}\right)P\left({B}^{\text{'}}\right)$(as $A$ and $B$ are independent)

$\left[1-P\left(A\right)\right]\left[1-P\left(B\right)\right]\phantom{\rule{0ex}{0ex}}=\left(1-0.9\right)\left(1-0.8\right)\phantom{\rule{0ex}{0ex}}=0.1\left(0.2\right)\phantom{\rule{0ex}{0ex}}=0.02$

Therefore the correct option is $\left(c\right)$

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