Question

Based on a science society study, there is a 0.9 probability that in the United States, a randomly selected dollar bill is tainted with traces of cocaine. Assume that eight dollar bills are randomly selected. Use calculator or technology to solve the following questions and make sure you apply round-off rule correctly:

(a) Find the probability that all of them have traces of cocaine.

(b) Find the probability that exactly seven of them have traces of cocaine.

(c) Find the probability that the number dollar bills with traces of cocaine is six or more.

(d) If we randomly select eight dollar bills, is five an unusually low number for those with traces of cocaine? Why?

Answer 1

Binomial probability:

P(X) = n!/(X!*(n−X)!)*p^X*(1−p)^(n−X)

a)

The probability that all of them have traces of cocaine

P(8) = 8!/8!*(8−8)!*0.9^8*(1−0.9)^(8−8)

P(8) = 0.4305

b)

The probability that exactly seven of them have traces of cocaine

P(7) = 8!/7!*(8−7)!*0.9^7*(1−0.9)^(8−7)

P(7) = 0.3826

c)

The probability that the number dollar bills with traces of cocaine is six or more

P(X ≥ 6) = P(6) + P(7) + P(8)

P(6) = 8!/6!*(8−6)!*0.9^6*(1−0.9)^(8−6) = 0.1488

P(7) = 0.3826

P(8) = 0.4305

P(X ≥ 6) = 0.14880348 + 0.38263752 + 0.43046721 = 0.9619

d)

Yes