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?

A. 4/95
B. 10/25
C. 39/95
D. 1/25

Answer 1

To find the probability of selecting a yellow marble 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.

\[
P(\text{Yellow}) = \frac{4}{20} = \frac{1}{5}
\]

2. **Calculate the probability of selecting a purple marble second.**
After selecting a yellow marble, there are now 19 marbles left in the jar (20 - 1 = 19). The number of purple marbles remains the same, which is still 4.

\[
P(\text{Purple | Yellow}) = \frac{4}{19}
\]

3. **Combine the probabilities.**
The probability of both events occurring (selecting a yellow marble first and then a purple marble) can be found by multiplying the two 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 without replacement and then selecting a purple marble is

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

The correct answer is **A. 4/95**.