Question

5. There are 10 cereal boxes on the store shelf. 4 of the boxes are known to have prizes. You select 3 boxes. Use four decimal places a. What probability distribution works best for this problem? Binomial, Poisson, Hypergeometric, Normal b. What is the expected number of selected cereal boxes with prizes? (2 decimal places) c. What is the probability you get 1 prize? (4 decimal places) d. What the probability you get 2 prizes? (4 decimal places) e. What the probability you get no prizes? (4 decimal places)

Answer 1

We have , there are total number of cereal boxes on the store shelf is 10

Let , X be the number of cereal boxes are known to have prizes.

Let , p be the probability that the cereal boxes are known to have prizes.

Here , p=X/n=4/10=0.4

Now , we randomly selected 3 boxes.

a) Here , X has binomial distribution with parameter n=3 and p=0.4

Therefore , the probability mass function of X is ,

; x=0,1,.........,n and q=1-p

= 0 ; otherwise

b) E(X)=np=3*0.4=1.20

Therefore , the expected number of selected cereal boxes with prizes is 1.20

c) P(X=1)=0.4320 ; From Binomial probability table

Therefore , the probability that you get 1 prize is 0.4320

d) P(X=2)=0.2880 : From Binomial probability table

Therefore , the probability that you get 2 prize is 0.2880

e) P(X=0)=0.2160 ; From Binomial probability table

Therefore , the probability that you get no prize is 0.2160