Question

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

332
Start Fraction 3 over 32 End Fraction

173240
Start Fraction 173 over 240 End Fraction

1116
Start Fraction 11 over 16 End Fraction

110

Answer 1

To find the probability of selecting a blue marble first and then, without replacing it, selecting a yellow marble, we can follow these steps:

1. **Calculate the probability of selecting a blue marble:**
There are 3 blue marbles out of a total of 16 marbles, so the probability of selecting a blue marble is:
\[
P(\text{Blue}) = \frac{3}{16}
\]

2. **Calculate the probability of selecting a yellow marble after removing a blue marble:**
Once the blue marble is drawn, there are now 15 marbles left in the jar (16 - 1 = 15). The number of yellow marbles remains the same at 8. Thus, the probability of now selecting a yellow marble is:
\[
P(\text{Yellow | Blue}) = \frac{8}{15}
\]

3. **Calculate the combined probability:**
We multiply the probabilities of both events occurring:
\[
P(\text{Blue and then Yellow}) = P(\text{Blue}) \times P(\text{Yellow | Blue}) = \frac{3}{16} \times \frac{8}{15}
\]

Calculating this gives:
\[
P(\text{Blue and then Yellow}) = \frac{3 \times 8}{16 \times 15} = \frac{24}{240} = \frac{1}{10}
\]

Now let's match this with the options provided to see if any correspond to \( \frac{1}{10} \):

- \( \frac{3}{32} \) does not match.
- \( \frac{173}{240} \) does not match.
- \( \frac{11}{16} \) does not match.
- \( \frac{1}{10} \) is not explicitly listed.

None of the options provided match the calculated probability of \( \frac{1}{10} \). Please double-check the options available or the parameters of the problem. The correct answer based on the calculations is \( \frac{1}{10} \).