Question

1 fill in the blank 8 points one marble is randomly drawn and then replaced from a jar containing two white marbles and one black marble. a second marble is drawn. what is the probability of drawing a white and then a black? write the answer as a fraction in simplest form. type your answer...

Explanation:

Step1: Find probability of white

Total marbles: \(2 + 1 = 3\). White marbles: \(2\). So \(P(\text{white}) = \frac{2}{3}\).

Step2: Find probability of black

After replacement, total marbles still \(3\). Black marbles: \(1\). So \(P(\text{black}) = \frac{1}{3}\).

Step3: Multiply probabilities

Since events are independent, \(P(\text{white then black}) = \frac{2}{3} \times \frac{1}{3} = \frac{2}{9}\).

Answer:

\(\frac{2}{9}\)