Answer
E(x) = $\frac{8}{5}$
Work Step by Step
The probability of selecting green marbles $= \frac{2}{5}$
R = red, G = green
P(x=0) → RRRR →$(\frac{3}{5})^{4}$
P(x=1) → GRRR, RGRR, RRGR, RRRG = $4(\frac{2}{5})(\frac{3}{5})^{3}$
P(x=2) → RRGG, GGRR, RGGR, GRRG, GRGR, RGRG = $6(\frac{2}{5})^{2}(\frac{3}{5})^{2}$
P(x=3) → GGGR, RGGG, GRGG, GGRG = $4(\frac{2}{5})^{3}(\frac{3}{5})$
P(x=4) → GGGG = $(\frac{2}{5})^{4}$
E(x) = $0\times (\frac{2}{5})^{4}+1\times 4(\frac{2}{5})(\frac{3}{5})^{3}+2\times 6(\frac{2}{5})^{2}(\frac{3}{5})^{2} +3\times 4(\frac{2}{5})^{3}(\frac{3}{5}) +4\times (\frac{2}{5})^{4} = \frac{8}{5}$