Question

One marble is randomly drawn and then replaced from a jarcontaining two white marbles and one black marble. A secondmarble is drawn. What is the probability of drawing a white andthen a black?

Answer 1

Event A: drawing a white marble

Event B: drawing a blck marble

Probability of drawing a white and then a black (with replacement:

`\begin{gathered} P(A,B)=P(A)*P(B) \\ \\ P(A,B)=\frac{#white\text{ }marbles}{#marbles}*\frac{#black\text{ }marbles}{#marbles} \\ \\ P(A,B)=(2)/(3)*(1)/(3) \\ \\ P(A,B)=(2)/(9) \end{gathered}`

Then, the probability of drawing a white and then a black is 2/9