Question

a bag contains 5 marbles: 2 red, 3 blue. if 1 marble is drawn, replaced, and 1 is drawn again, what is the probability of drawing a red marble both times? event a: red marble on 1st draw event b: red marble on 2nd draw p(a, then b) =? compound probability independent events p(a, then b) = p(a) · p(b) give your answer as a fraction in simplest form.

Explanation:

Step1: Calculate P(A)

Probability of red on first draw: $\frac{2}{5}$

Step2: Calculate P(B)

Probability of red on second draw (replaced): $\frac{2}{5}$

Step3: Multiply probabilities

$P(A \text{ then } B) = \frac{2}{5} \times \frac{2}{5} = \frac{4}{25}$

Answer:

$\frac{4}{25}$