Question

In Hawaii, the rate of motor vehicle theft is 435 thefts per 100,000 vehicles. A large parking structure in Honolulu has issued 526 parking permits. (a) What is the probability that none of the vehicles with a permit will eventually be stolen? (Round ? to 1 decimal place. Use 4 decimal places for your answer.) (b) What is the probability that at least one of the vehicles with a permit will eventually be stolen? (Use 4 decimal places.) (c) What is the probability that three or more vehicles with a permit will eventually be stolen? (Use 4 decimal places.)

Answer 1

here expected thefts =435*526/100000=2.3=

a)

probability that none of the vehicles with a permit will eventually be stolen=P(X=0)

=e^-2.3*2.3⁰/0!=0.1003

b) probability that at least one of the vehicles with a permit will eventually be stolen

=P(X>=1)=1-P(X=0)=1-0.1003=0.8997

c)probability that three or more vehicles with a permit will eventually be stolen=P(X>=3)

=1-P(X<=2)=1-(P(X=0)+P(X=1)+P(X=2))=1-(e^-2.3*2.3⁰/0!+e^-2.3*2.3¹/1!+e^-2.3*2.3²/2!)

=1-0.5960=0.4040