$\begin {array} {1 1} (A)\;\large\frac{291}{364} & \quad (B)\;\large\frac{371}{464} \\ (C)\;\large\frac{471}{502} & \quad (D)\;\large\frac{459}{512} \end {array}$

Using binomial distribution we have to find $ P(3) +P(4)+P(5)$

This probability is

$ 5C_3 \bigg( \large\frac{3}{4} \bigg)^3\bigg( \large\frac{1}{4} \bigg)^2+5C_4\bigg( \large\frac{3}{4} \bigg)^4\bigg( \large\frac{1}{4} \bigg)^1+5C_5\bigg( \large\frac{3}{4} \bigg)^5\bigg( \large\frac{1}{4} \bigg)^0$

$= \large\frac{270+405+243}{45} = \large\frac{918}{1024}$

$ = \large\frac{459}{512}$

Ans : (D)

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