Question

1) You throw darts at a board until you hit the center area. Your probability of hitting the center area is p=0.17. You want to find the probability that on the 4th throw you hit the center

2) A wallet contains 3 $100 bills and 5 $1 bills. You randomly choose 4 bills. What is the probability that you will choose exactly 2 $100 bills?

3) The mean number of defective products produced in a factory in one day is 21. What is the probability that in a given day there are exactly 12 defective products?

Answer 1

1)

P(hitting) = 0.17

P( not hitting) = 0.83

the probability that on the 4th throw you hit

= P( not hitting) * P( not hitting) *P( not hitting) *P( hitting)

= 0.83*0.83*0.83*0.17 = 0.097

2)

No of ways to selecting 2 in total 3+5 = 8 biils

selecting 2 100 bills and 2 1 bills

the probability that you will choose exactly 2 $100 bills = 30/70 = 0.429

3)

By Poisson distribution with mean 21

P(X=12) = 0.0116