Question

Consider a jar that has 20 marbles. There are 4 red, 4 blue, 4 green, 4 yellow, and 4 purple marbles. What is the probability of selecting a yellow marble without replacing it and then selecting a purple marble?(1 point)
Responses

125
Start Fraction 1 over 25 End Fraction

3995
Start Fraction 39 over 95 End Fraction

495
Start Fraction 4 over 95 End Fraction

1025
Start Fraction 10 over 25 End Fraction

Answer 1

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

1. **Determine the total number of marbles and the number of yellow marbles.**
- Total marbles: 20
- Yellow marbles: 4

2. **Calculate the probability of selecting a yellow marble first.**
\[
P(\text{yellow}) = \frac{\text{Number of yellow marbles}}{\text{Total number of marbles}} = \frac{4}{20} = \frac{1}{5}
\]

3. **Now, determine the total number of marbles remaining after removing one yellow marble.**
- After selecting one yellow marble, the remaining total is \(20 - 1 = 19\) marbles.
- The number of purple marbles is still \(4\).

4. **Calculate the probability of selecting a purple marble next.**
\[
P(\text{purple | yellow selected}) = \frac{\text{Number of purple marbles}}{\text{Total number of remaining marbles}} = \frac{4}{19}
\]

5. **Now multiply the probabilities to find the combined probability of both events occurring.**
\[
P(\text{yellow and then purple}) = P(\text{yellow}) \times P(\text{purple | yellow selected}) = \frac{1}{5} \times \frac{4}{19}
\]

6. **Performing the multiplication:**
\[
P(\text{yellow and then purple}) = \frac{1 \times 4}{5 \times 19} = \frac{4}{95}
\]

Therefore, the probability of selecting a yellow marble first and then a purple marble without replacement is:

\[
\frac{4}{95}
\]

So, the correct answer is:
**Start Fraction 4 over 95 End Fraction**.