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

495
Start Fraction 4 over 95 End Fraction

3995
Start Fraction 39 over 95 End Fraction

1025
Start Fraction 10 over 25 End Fraction

125

Answer 1

To determine the probability of selecting a yellow marble first and then a purple marble from the jar without replacement, we can follow these steps:

1. **Determine the total number of marbles**: The jar has 20 marbles in total.

2. **Calculate the probability of selecting a yellow marble first**: There are 4 yellow marbles out of 20. Thus, the probability of selecting a yellow marble is:
\[
P(\text{Yellow}) = \frac{4}{20} = \frac{1}{5}
\]

3. **Calculate the probability of selecting a purple marble second**: Once a yellow marble has been selected, there are now 19 marbles left in the jar, including 4 purple marbles. The probability of now selecting a purple marble is:
\[
P(\text{Purple | Yellow taken}) = \frac{4}{19}
\]

4. **Combine the probabilities**: The overall probability of selecting a yellow marble first and then a purple marble is the product of the two probabilities:
\[
P(\text{Yellow and then Purple}) = P(\text{Yellow}) \times P(\text{Purple | Yellow taken}) = \frac{4}{20} \times \frac{4}{19} = \frac{1}{5} \times \frac{4}{19} = \frac{4}{95}
\]

Thus, the probability of selecting a yellow marble without replacing it and then selecting a purple marble is:
\[
\frac{4}{95}
\]

Therefore, the correct answer is:

**Start Fraction 4 over 95 End Fraction**