An insurance company receives 40 claims in a certain month. Company policy mandates that a random selection of 5 of these claims be thoroughly investigated. If 3 of the 40 claims are fraudulent, find the probability that none of the fraudulent claims are thoroughly investigated. Round your answer to three decimal places.
A)0.025
B)0.001
C)0.662
D)0.493

Question

An insurance company receives 40 claims in a certain month. Company policy mandates that a random selection of 5 of these claims be thoroughly investigated. If 3 of the 40 claims are fraudulent, find the probability that none of the fraudulent claims are thoroughly investigated. Round your answer to three decimal places. ​
A)0.025
B)0.001
C)0.662
D)0.493

Quizplus · Accepted Answer

The probability of selecting 5 claims out of 40 is given by the combination formula:

C(40,5) = 40!/(5!35!) = 40*39*38*37*36/(5*4*3*2*1) = 658008

The probability of selecting no fraudulent claims out of the 37 non-fraudulent claims is:

C(37,5) = 37!/(5!32!) = 37*36*35*34*33/(5*4*3*2*1) = 376992

Therefore, the probability of selecting none of the fraudulent claims is:

P = 376992/658008 = 0.662 (rounded to three decimal places)

So, the best choice is C.

An Insurance Company Receives 40 Claims in a Certain Month