Question

There are five marbles in a bag. Three are green and two are yellow. You draw a marble, replace it, and then draw another. What is the probability of choosing two yellow marbles?

4/25


1/10

2/5

1/5

Answer 1

To determine the probability of drawing two yellow marbles in a row (with replacement), we first find the probability of drawing a yellow marble on a single draw.

There are a total of 5 marbles: 3 green and 2 yellow.

The probability of drawing a yellow marble on the first draw is:
\[
P(\text{Yellow}) = \frac{\text{Number of yellow marbles}}{\text{Total number of marbles}} = \frac{2}{5}
\]

Since we are replacing the marble after the first draw, the probabilities remain the same for the second draw. Therefore, the probability of drawing a yellow marble on the second draw is also:
\[
P(\text{Yellow}) = \frac{2}{5}
\]

The probability of both events (drawing a yellow marble both times) occurring is the product of their individual probabilities:
\[
P(\text{Two yellow marbles}) = P(\text{Yellow on first draw}) \times P(\text{Yellow on second draw}) = \frac{2}{5} \times \frac{2}{5} = \frac{4}{25}
\]

Thus, the probability of choosing two yellow marbles is:
\[
\frac{4}{25}
\]

Therefore, the answer is \(\frac{4}{25}\).