Question

heather has a bag containing 4 marbles: 1 red, 1 blue, and 2 green. she draws 1 marble out of the bag, replaces it, and then draws another marble. what is p(red then blue then green)? \\(\frac{1}{64}\\) \\(\frac{1}{32}\\) \\(\frac{1}{2}\\) \\(\frac{3}{4}\\)

Explanation:

Step1: Find P(red)

There are 4 marbles, 1 red. So \( P(\text{red}) = \frac{1}{4} \).

Step2: Find P(blue)

1 blue marble, so \( P(\text{blue}) = \frac{1}{4} \).

Step3: Find P(green)

2 green marbles, so \( P(\text{green}) = \frac{2}{4}=\frac{1}{2} \).

Step4: Multiply the probabilities

Since the draws are independent (with replacement), \( P(\text{red then blue then green}) = P(\text{red}) \times P(\text{blue}) \times P(\text{green}) \).
Substitute the values: \( \frac{1}{4} \times \frac{1}{4} \times \frac{1}{2} = \frac{1}{32} \).

Answer:

\(\frac{1}{32}\) (corresponding to the option with \(\frac{1}{32}\))