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

3995
Start Fraction 39 over 95 End Fraction

125
Start Fraction 1 over 25 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 replacement, we can break it down into two steps.

1. **Selecting a yellow marble:**
- There are 4 yellow marbles out of a total of 20 marbles.
- The probability of selecting a yellow marble first is:
\[
P(\text{yellow}) = \frac{4}{20} = \frac{1}{5}
\]

2. **Selecting a purple marble after a yellow marble has been selected:**
- After removing a yellow marble, there are now 19 marbles left in the jar (20 - 1).
- The number of purple marbles remains 4.
- The probability of selecting a purple marble after selecting a yellow marble is:
\[
P(\text{purple | yellow}) = \frac{4}{19}
\]

Now, we can find the combined probability of both events occurring:

\[
P(\text{yellow and then purple}) = P(\text{yellow}) \times P(\text{purple | yellow}) = \frac{1}{5} \times \frac{4}{19} = \frac{4}{95}
\]

Thus, the probability of selecting a yellow marble and then a purple marble is:

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

Among the provided options, the correct answer is:
\[
\frac{4}{95}
\]