Question

A bag of contains 4 blue marbles, 6 green marbles and 3 yellow marbles. If two marbles are drawn at random from the bag, whats the probability of:

Drawing 2 blue marbles? With Replacement


.095


.106


.086


.073

Answer 1

To find the probability of drawing 2 blue marbles with replacement from the bag, we first need to determine the total number of marbles in the bag.

Total marbles = 4 (blue) + 6 (green) + 3 (yellow) = 13 marbles.

When we draw with replacement, the probability of drawing a blue marble remains constant for each draw.

1. **Probability of drawing the first blue marble:**
\[
P(\text{blue}) = \frac{4 \text{ (blue marbles)}}{13 \text{ (total marbles)}} = \frac{4}{13}
\]

2. **Probability of drawing the second blue marble (since it's with replacement, the probability remains the same):**
\[
P(\text{blue}) = \frac{4}{13}
\]

3. **Probability of drawing 2 blue marbles:**
Since the events are independent (due to replacement), we multiply the probabilities:
\[
P(\text{2 blue marbles}) = P(\text{blue}) \times P(\text{blue}) = \frac{4}{13} \times \frac{4}{13} = \frac{16}{169}
\]

4. **Calculating the fraction:**
Now, let's convert \(\frac{16}{169}\) into a decimal:
\[
\frac{16}{169} \approx 0.0947
\]

Rounded to three decimal places, this is approximately \(0.095\).

Thus, the probability of drawing 2 blue marbles with replacement is:

**0.095** (the first option listed).