Question

Suppose we pick 3 students at random from a class with 10 boys and 15 girls. let x be the number of boys selected and y be the number of girls selected. find e(x-y

Answer 1

The probability of the first pick to be a boy is 10/25.
Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
n(S)=number of ways selecting students of 25.
=²⁵C₃
=25·24·23/3·2·1
=2300
n(E)=(¹⁰C₁·¹⁵C₂)
=[10·(15·14)/2·1
=10500
P(E)=n(E)/n(S)=1050/2300=21/46