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

3995
Start Fraction 39 over 95 End Fraction

495
Start Fraction 4 over 95 End Fraction

125
Start Fraction 1 over 25 End Fraction

1025

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.
2. Calculate the probability of selecting a purple marble second, given that a yellow marble has already been selected.
3. Multiply the probabilities together.

**Step 1: Probability of selecting a yellow marble first**

There are 4 yellow marbles out of a total of 20 marbles.

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

**Step 2: Probability of selecting a purple marble second**

After selecting a yellow marble, there will be 19 marbles left in the jar. The number of purple marbles remains 4.

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

**Step 3: Multiply the probabilities**

Now, we multiply the probabilities from Step 1 and Step 2 to get the overall probability:

\[
P(\text{Yellow then Purple}) = P(\text{Yellow}) \times P(\text{Purple | Yellow}) = \frac{1}{5} \times \frac{4}{19} = \frac{4}{95}
\]

So, 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**