a) $P\left( {X = 1} \right) = P\left( {GBBB} \right)4 \times {C_1}$
$ = 5/8 \times 3/7 \times 2/6 \times 1/5 \times 4 = 1/14$
$P\left( {X = 2} \right) = P\left( {GGBB} \right) \times {}_4{C_2} = 3/7$
$P\left( {X = 3} \right) = P\left( {GGGB} \right) \times {}_4{C_3} = 3/7$
$P\left( {X = 4} \right) = P\left( {GGGG} \right) \times {}_4{C_4} = 1/14$
OR
$P\left( 1 \right) = {}_5{C_1}/{}_8{C_4} = 1/14$
$P\left( 2 \right) = {}_3{C_2} \times {}_5{C_2}/{}_8{C_4} = 3/7$
$P\left( 3 \right) = {}_3{C_1} \times {}_5{C_3}/{}_8{C_4} = 3/7$
$P\left( 4 \right) = {}_5{C_4}/{}_8{C_4} = 1/14$
b) $Var\left( X \right) = 1/14 + 12/7 + 27/7 + 16/14 - {\left( {5/2} \right)^2}$
$ = 15/28{\text{ }}\left( {0.536} \right)$