U is underweight, N is not-underweight
a) so you want UUUU = (.18)(.18)(.18)(.18)
= .18^4 = .00105
b) wouldn't that be all not-underweight ?
or (.82)^4 = .45212
c) at least one underweight implies
1 - Prob(all non-overweight)
= 1-.45212
Since there are only 5 cases possible, I will do each one to show the logic of the above
none underweight = (.82)^4 = .45212
1 underweight = C(4,1)(.18)(.82)^3 = .39698
2 underweight = C(4,2)(.18)^2(.82)^2 = .13071
3 underweight = C(4,3)(.18)^3(.82) = .01913
4 underweight = (.18)^4 = .00105
notice if we total this we get 1
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c. at least one will be underweight
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