Probability of White Balls

In the first container, we have 3 white and 6 black balls. In the second container, we have 2 white and 6 black balls. We randomly transfer 1 ball from the first container to the second container. What is the probability that I then pick 2 white marbles from the second jar?

Final Answer:

p =  0.2917

Step-by-step explanation:

$$\begin{gathered} p_1=\frac{3}{6}=\frac{1}{2}=0.5 \\ p=p_1\cdot \frac{2+1}{6+2+1}+(1-p_1)\cdot \frac{2}{2+6}=\frac{1}{2}\cdot \frac{2+1}{6+2+1}+(1-\frac{1}{2})\cdot \frac{2}{2+6}=\frac{7}{24}=0.2917 \end{gathered}$$

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