Question 1023297
{{{P(X)=C(3,X)*(5/20)^X*(1-5/20)^(3-X)}}}
{{{P(X)=C(3,X)*(1/4)^X*(3/4)^(3-X)}}}
1. All graduates {{{X=3}}}
{{{P(3)=C(3,3)*(1/4)^3*(3/4)^(3-3)}}}
{{{P(3)=1*(1/64)*1}}}
{{{P(3)=1/64}}}
2. No graduates {{{X=0}}}
{{{P(0)=C(3,0)*(1/4)^0*(3/4)^(3-0)}}}
{{{P(0)=1*1*(27/64)}}}
{{{P(0)=27/64}}}
3. Two graduates {{{X=2}}}
{{{P(2)=C(3,2)*(1/4)^2*(3/4)^(3-2)}}}
{{{P(2)=3*(1/16)*(3/4)}}}
{{{P(2)=9/64}}}
4. At most one, {{{X=0}}} and {{{X=1}}}
{{{P(1)=C(3,1)*(1/4)^1*(3/4)^(3-1)}}}
{{{P(1)=3*(1/4)*(9/16)}}}
{{{P(1)=27/64}}}
So,
{{{P=P(0)+P(1)}}}
{{{P=27/64+27/64}}}
{{{P=27/32}}}
5. At least one, {{{X=1}}}, {{{X=2}}}, and {{{X=3}}}
{{{P=P(1)+P(2)+P(3)}}}
{{{P=27/64+9/64+1/64}}}
{{{P=37/64}}}
6. Two non-graduates is the same as one graduate.
{{{P(1)=27/64}}}