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

125
Start Fraction 1 over 25 End Fraction

1025
Start Fraction 10 over 25 End Fraction

3995

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. **Probability of selecting a yellow marble:**
There are 4 yellow marbles out of a total of 20 marbles.
\[
P(\text{Yellow}) = \frac{4}{20} = \frac{1}{5}
\]

2. **Probability of selecting a purple marble after selecting a yellow marble:**
After selecting a yellow marble, there will be 19 marbles left in total (since we are not replacing the yellow marble), and still 4 purple marbles.
\[
P(\text{Purple} | \text{Yellow}) = \frac{4}{19}
\]

Now, to find the combined probability of these two events happening in sequence, we multiply the probabilities:
\[
P(\text{Yellow and then Purple}) = P(\text{Yellow}) \times P(\text{Purple} | \text{Yellow}) = \frac{1}{5} \times \frac{4}{19} = \frac{4}{95}
\]

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

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

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