Let. X = Prob. that a good mango is selected = 18/24= 3/4
Y Prob. that a bad mango is selected = 6/24 1/4
Using the binomial probability distribution, we have:
(X+Y)${}^6$ = X${}^6$ + ${}^6{C}_1{X}^{5}Y$ + ${}^6{C}_2{X}^4{Y}^2$ + ${}^6{C}_3{X}^3{Y}^3$ + ${}^6{C}_4{X}^2{Y}^4$ + ${}^6{C}_{5}X{Y}^5$ + ${}^6{C}_6{Y}^6$
Probability that not more than 3 are bad is
= ${}^6{C}_1{X}^{5}Y$ + ${}^6{C}_2{X}^4{Y}^2$ + ${}^6{C}_3{X}^3{Y}^3$
= 6(3/4)${}^5$ (1/4) + 15(3/4)${}^4$ (1/4)${}^2$ + 20(3/4)${}^3$ (1/4)${}^3$
= 6(243/1024)(1/4) + 15(81/256)(1/16) + 20(27/64)(1/64)
= 0.36 + 0.30 + 0.13
≈ 0.79