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

1025
Start Fraction 10 over 25 End Fraction

495
Start Fraction 4 over 95 End Fraction

3995

Answer 1

To find the probability of selecting a yellow marble followed by 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 and a total of 20 marbles.
- Probability of selecting a yellow marble:
\[
P(\text{Yellow}) = \frac{4}{20} = \frac{1}{5}
\]

2. **Calculate the probability of selecting a purple marble second, after a yellow marble has already been selected.**
- After selecting one yellow marble, there are now 19 marbles left, with still 4 purple marbles remaining.
- Probability of selecting a purple marble now:
\[
P(\text{Purple | Yellow}) = \frac{4}{19}
\]

3. **Calculate the combined probability of both events happening in sequence.**
- Since the events are sequential, we multiply the probabilities:
\[
P(\text{Yellow then Purple}) = P(\text{Yellow}) \cdot P(\text{Purple | Yellow}) = \frac{1}{5} \cdot \frac{4}{19} = \frac{4}{95}
\]

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

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

The correct answer is **Start Fraction 4 over 95 End Fraction**.