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?(7 points)
Responses

3995
39 over 95

495
4 over 95

125
1 over 25

1025

Answer 1

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

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

2. **Calculate the probability of selecting a purple marble second**:
- Once a yellow marble has been chosen, there are now 19 marbles left in the jar (20 - 1 = 19).
- There are still 4 purple marbles in the jar.
- The probability of selecting a purple marble now is:
\[
P(\text{Purple | Yellow}) = \frac{4}{19}
\]

3. **Calculate the combined probability of both events happening**:
- We find the combined probability by multiplying the two individual probabilities together:
\[
P(\text{Yellow and then Purple}) = P(\text{Yellow}) \times P(\text{Purple | Yellow}) = \frac{1}{5} \times \frac{4}{19} = \frac{4}{95}
\]

Thus, the probability of selecting a yellow marble first and then a purple marble is \(\frac{4}{95}\).

The correct response is:

**4 over 95**.