List elementary outcomes, assign probabilities, etc

[trackgirl000]

A salesman of home computers will contact four customers during a week. Each contact can result in either a sale, with probability 0.2, or no sale, with a probability 0.8. Assume that customer contacts are independent.

a. List the elementary outcomes and assign probabilities
b. If X denotes the number of computers sold during the week, obtain the probability distribution of X.
c. Calculate the expected value of X.

thanks a lot.

 

[arthur ohlsten]

P=.2 Q=.8
where P is a sale and Q no saleet
1)
[P+Q]^4=P^4+4P^3Q+6P^2Q^2+4PQ^3+Q^4
P[4]=[.2]^4
P[3]=4[.2]^3[.8]
P[2]=6[.2]^2[.8]^2
P[1]=4[.2][.8]^3
P[0]=[.8]^4

2)
P[x]=4Cx P^xQ^(4-x)

3)
expected value=sum xP[x]
expected value=0[.8]^4+1[4][.2][.8]^3 +2[6][.2]^2[.8]^2+3[4][.2]^1[.8]^3+4[.8]^4
expected value= .4096+.3076+1.228+1.6384
expected value= 3.5
this appears to be wrong, answer should be closer to 1 sale
Arthur