Question

One day, Professor brought a box that contains 6 yellow and 7 green marbles in his class in Statistics and Probability subject. He asked one student to draw three marbles, with replacement, in the box. What is the probability when the student drawn 1 yellow and 2 green marbles? Convert your answer in decimals with three (3) significant figures.

Answer 1

$$P(Y)=\dfrac{6}{6+7}=\dfrac{6}{13}$$

$$P(G)=\dfrac{6}{6+7}=\dfrac{7}{13}$$

$$P(YGG)=\dfrac{6}{13}(\dfrac{7}{13})(\dfrac{7}{13})=\dfrac{294}{2197}$$

$$P(GYG)=\dfrac{7}{13}(\dfrac{6}{13})(\dfrac{7}{13})=\dfrac{294}{2197}$$

$$P(GGY)=\dfrac{7}{13}(\dfrac{7}{13})(\dfrac{6}{13})=\dfrac{294}{2197}$$

$$P(1Y\ and \ 2G)=\dfrac{294}{2197}+\dfrac{294}{2197}+\dfrac{294}{2197}\approx0.401$$