Question

A bag contains $7$ green, $4$ white and $5$ red balls. If four balls are drawn one by one with replacement. What is the probability that one is red?

Answer 1

Red ball may be drawn at any of the four draws

$\Rightarrow (\frac{5}{16}\times \frac{11}{16}\times \frac{11}{16}\times \frac{11}{16}){\times }^4{C}_1$

$\to$ where $\frac{5}{16}$ is the probability of drawing a red ball and $\frac{11}{16}$ is the probability of not drawing a red ball for each draw

$\Rightarrow \frac{5\times {11}^3}{{16}^3\times 16}\times 4$

$=\frac{6655}{16384}=0.41$