1) A lottery game has thefollowing rules: pick 6 distinct numbers from a set of4

ID: 2954814 • Letter: 1

Question

1) A lottery game has thefollowing rules: pick 6 distinct numbers from a set of49.

The grand prize winner picks 6numbers out of 6 correctly.

(i) What is the probability ofwinning the grand prize?

Manyprofessional sports leagues test their players for steroids. Manyplayers

that testpositive for steroid use claim that their test is a ‘falsepositive,” that is,

the test cameup positive for steroid use when the player has not actuallyused

steroids.Suppose that an anonymous survey reveals that 30% of all playersin

the leaguetake steroids. The company that designs the drug test claims thatthe

testcorrectly identifies drug use (as well as non-use) 99% of the time.Find the

probabilitythat the test incorrectly identifies a steroid user when the playerhas

truly never usedsteroids.

1) A lottery game has thefollowing rules: pick 6 distinct numbers from a set of49.

The grand prize winner picks 6numbers out of 6 correctly.

(i) What is the probability ofwinning the grand prize?

choose 6 winning numbers=6*5*4*3*2*1=

choose 6 number from 49 =49*48*47*46*45*44=6.08281864*1062

Probability ofwinning 720/6.08281864*1062=1.18366179*10-60

Manyprofessional sports leagues test their players for steroids. Manyplayers

that testpositive for steroid use claim that their test is a ‘falsepositive,” that is,

the test cameup positive for steroid use when the player has not actuallyused

steroids.Suppose that an anonymous survey reveals that 30% of all playersin

the leaguetake steroids. The company that designs the drug test claims thatthe

testcorrectly identifies drug use (as well as non-use) 99% of the time.Find the

probabilitythat the test incorrectly identifies a steroid user when the playerhas

truly never usedsteroids.

p(of not a steroiduser)=.70

P(of testwrong)=.01

these areindependent

P(of not a steroid userand test wrong)= .7(.01)=.007

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