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Q. 103.

Expert-verifiedFound in: Page 337

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 required answer is:

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

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.

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" $B.$

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

$P\left(A\hat{a}<{B}^{\text{'}}\right)=P\left({A}^{\text{'}}\right)P\left({B}^{\text{'}}\right)$(as $A$ and $B$ are independent)$\left[1-P\left(A\right)\right]\left[1-P\left(B\right)\right]\phantom{\rule{0ex}{0ex}}=(1-0.9)(1-0.8)\phantom{\rule{0ex}{0ex}}=0.1(0.2)\phantom{\rule{0ex}{0ex}}=0.02$

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

Butter side down Refer to the preceding exercise. Maria decides to test this

probability and drops $10$ pieces of toast from a $2.5$-foot table. Only $4$ of them land butter

side down. Maria wants to perform a simulation to estimate the probability that $4$ or

fewer pieces of toast out of $10$ would land butter side down if the researchers’ $0.81$

probability value is correct.

a. Describe how you would use a table of random digits to perform the simulation.

b. Perform $3$ trials of the simulation using the random digits given. Copy the digits onto

your paper and mark directly on or above them so that someone can follow what you

did.

$29077$ | $14863$ | $61683$ | $47052$ | $62224$ | $51025$ |

$95052$ | $90908$ | $73592$ | $75186$ | $87136$ | $95761$ |

$27102$ | $56027$ | $55892$ | $33063$ | $41842$ | $81868$ |

c. The dotplot displays the results of 50 simulated trials of dropping $10$ pieces of toast.

Is there convincing evidence that the researchers’ $0.81$probability value is incorrect?

Explain your answer.

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