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 correct calculation for the probability of selecting a yellow marble without replacing it and then selecting a purple marble?(1 point)
Responses

4
20
+
4
20
Start Fraction 4 over 20 End Fraction plus Start Farction 4 over 20 End Fraction

4
20
⋅
4
19
Start Fraction 4 over 20 End Fraction times Start Farction 4 over 19 End Fraction

4
20
⋅
4
20
Start Fraction 4 over 20 End Fraction times Start Farction 4 over 20 End Fraction

4
20
+
4
19

Answer 1

To find the probability of selecting a yellow marble without replacement and then selecting a purple marble, we need to calculate the probability of each event happening sequentially.

1. The probability of selecting a yellow marble first:
\[
P(\text{Yellow}) = \frac{4}{20}
\]

2. After selecting a yellow marble, there are now 19 marbles left in the jar (since one marble has been removed). The probability of then selecting a purple marble is:
\[
P(\text{Purple} \mid \text{Yellow}) = \frac{4}{19}
\]

Now, since these two selections are dependent events, we multiply the probabilities:
\[
P(\text{Yellow and then Purple}) = P(\text{Yellow}) \times P(\text{Purple} \mid \text{Yellow}) = \frac{4}{20} \times \frac{4}{19}
\]

Thus, the correct calculation is:
\[
\frac{4}{20} \cdot \frac{4}{19}
\]

Therefore, the response that correctly describes the calculation is:
\[
\frac{4}{20} \cdot \frac{4}{19}
\]