According to USA Today (March 18, 1997), of 4 million workers in the general wor

Question

According to USA Today (March 18, 1997), of 4

million workers in the general workforce, 5.8% tested

positive for drugs. Of those testing positive, 22.5%

were cocaine users and 54.4% marijuana users.

(a) What is the probability that of 10 workers testing

positive, 2 are cocaine users, 5 are marijuana users,

and 3 are users of other drugs?

(b) What is the probability that of 10 workers testing

positive, all are marijuana users?

solve this question using matlab binomial probability distribuion function and mulinomial probability distribion function.

(solve on matlab)

Explanation / Answer

(a)here we use multinomial distribution and with n=10, n1=2,p1=0.225,n2=5,p2=0.544,n3=3,p3=0.0231

required probability=(10!/(2!5!3!))*(0.225)2*(0..544)5*(0.231)3=0.0749

(b)here we use binomial distribution with n=10,p=0.544

required probability=10C10(0.544)10*(1-0.544)10-10=(0.544)10=0.0023

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