Question

There are 16 marbles in a jar: 5 red, 3 blue, and 8 yellow. What is the probability of selecting a blue marble and then, without replacing the blue marble, selecting a yellow marble?(1 point)
Responses

173240
Start Fraction 173 over 240 End Fraction

332
Start Fraction 3 over 32 End Fraction

110
Start Fraction 1 over 10 End Fraction

1116

Answer 1

To calculate the probability of selecting a blue marble and then a yellow marble without replacement, we can follow these steps:

1. **Find the total number of marbles**: There are 16 marbles in total (5 red + 3 blue + 8 yellow).

2. **Calculate the probability of selecting a blue marble first**:
\[
P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{16}
\]

3. **After selecting a blue marble, the total number of marbles left is 15** (since we do not replace the blue marble). The number of yellow marbles remains the same (8 yellow marbles).

4. **Calculate the probability of selecting a yellow marble after removing a blue marble**:
\[
P(\text{yellow | blue}) = \frac{\text{Number of yellow marbles}}{\text{Total number of remaining marbles}} = \frac{8}{15}
\]

5. **Calculate the combined probability of both events** (selecting a blue marble first, then a yellow marble):
\[
P(\text{blue and then yellow}) = P(\text{blue}) \times P(\text{yellow | blue}) = \frac{3}{16} \times \frac{8}{15}
\]

We can compute this step:
\[
P(\text{blue and then yellow}) = \frac{3 \times 8}{16 \times 15} = \frac{24}{240}
\]
Simplifying \(\frac{24}{240}\):
\[
\frac{24 \div 24}{240 \div 24} = \frac{1}{10}
\]

The correct probability of selecting a blue marble and then a yellow marble without replacement is:

\[
\boxed{\frac{1}{10}}
\]