Question

enter the correct answer.
a jar has 8 jellybeans: 5 red, 3 green. if 1 jellybean is randomly drawn, replaced, and then 1 is drawn again, what is the probability of getting red, then green?
event a: red on 1st draw
event b: green 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)

Total jellybeans = 8, red = 5. So $P(A) = \frac{5}{8}$.

Step2: Calculate P(B)

Total jellybeans remain 8 (replaced), green = 3. So $P(B) = \frac{3}{8}$.

Step3: Multiply probabilities

Independent events: $P(A \text{ then } B) = P(A) \cdot P(B) = \frac{5}{8} \cdot \frac{3}{8} = \frac{15}{64}$.

Answer:

$\frac{15}{64}$