In Hawaii, the rate of motor vehicle theft is 605 thefts per 100,000 vehicles. A

Question

In Hawaii, the rate of motor vehicle theft is 605 thefts per 100,000 vehicles. A large parking structure in Honolulu has issued 463 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.)

Explanation / Answer

P(vehicle being stolen) = 605/100000 = 0.00605

P(vehicle being safe) = (100000-605)/100000 = 0.99395

a)

P(X=0) = 0.99395^463 = 0.0602

b)

P(X>0) = 1- P(X=0) = 1- 0.0602 = 0.9398

c)

P(X>2) = 1 - (P(x=0) +P(x=1) +P(X=2))

1 - ( 0.99395^463+0.99395^462 *0.00605 + 2*0.99395^461*0.00605^2)

= 0.9394

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