*******PLEASE SHOW WORK...FORMULA******************** IN A FAMILY WITH 4 CHILDRE

Question

*******PLEASE SHOW WORK...FORMULA********************
IN A FAMILY WITH 4 CHILDREN, THE NUMBER OF CHILDREN WITH BLUE EYES IS A BINOMIAL RANDOM VARIABLE X WITH n=4 AND p=.20.

1.WHAT IS THE PROBABILITY THAT ALL 4 CHILDREN WILL HAVE BLUE EYES?

2. WHAT IS THE PROBABILITY THAT EXACTLY 3 CHILDREN WILL HAVE BLUE EYES?

3.WHAT IS THE PROBABILITY THAT NONE OF THE CHILDREN WILL HAVE BLUE EYES?

4.WHAT IS THE EXPECTED NUMBER OF CHILDREN WITH BLUE EYES, E(X)?

5.WHAT IS THE AVERAGE VARIANCE FOR THE NUMBER OF CHILDREN WITH BLUE EYES, V (X)?

Explanation / Answer

1. C(4,4)(.2^4)(.8^0)=.0016 2 . C(4,3)(.2^3)(.8^1)=.0064
3.C(4,0)(.2^0)(.8^4)=.4096 4. E(x)=np=4(.2)=.8
5. V(x)=npq=4(.2)(.8)=.64

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