In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date nonsmokers, 1% prefer to date smokers, and 21% don't care. suppose seven such boys are selected randomly. let x equal the number who prefer to date nonsmokers and y equal the number who prefer to date smokers.

the answer is PMF(x,y) = Prob{X prefer nonsmokers and Y prefer smokers}

Support: 0<=X<=7, 0<=Y<=7, 0<=X+Y<=7.

PMF = Combinations(X of 7) * Combinations(Y of 7-X) * 0.78^X * 0.01^Y * 0.21^(7-X-Y)

(b)

The marginal PMF comes from summing the joint PMF over over Y. Alternatively, we can get it directly:

Support: 0<=X<=7

PMF(X) = Combinations(X of 7) * (0.78)^X * (0.22)^(7-X)  

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x= cost per bracelet

number of bracelets * x + shipping charge = total cost

so

9x+9=72