A box contains a dozen markers: 4 purple, 3 black, 3 orange, and 2 red. Abbey takes 2 markers out of the box without looking. What is the probability that Abbey picks a black marker and then a purple marker if she replaces the first marker? Answer in simplest form.

prob(black, then purple)

= (3/12)(4/12) , denominator stays at 12, since she returned the marker.
= ....

To find the probability of Abbey picking a black marker and then a purple marker, we need to determine the probability of each event happening and then multiply them together.

First, let's find the probability of picking a black marker with replacement.

There are a total of 12 markers in the box, and 3 of them are black. Therefore, the probability of picking a black marker is 3/12.

Next, if Abbey replaces the first marker back into the box, the box still contains 12 markers. However, now there are 4 purple markers because the previous one is back in the box. So the probability of picking a purple marker is 4/12.

To find the probability of the two events happening together, we multiply their individual probabilities:

Probability of picking a black marker: 3/12
Probability of picking a purple marker: 4/12

Probability of both events happening = (3/12) * (4/12) = 12/144

Simplifying the fraction, we get:

Probability = 1/12

To find the probability of picking a black marker and then a purple marker, we need to calculate the probability of each event occurring individually and then multiply the probabilities together.

First, let's calculate the probability of picking a black marker on the first draw. There are a total of 12 markers in the box, so the probability of picking a black marker is 3 out of 12, or 3/12.

Since Abbey replaces the first marker, the probability of picking a purple marker on the second draw is also 4/12, as there are still 4 purple markers in the box.

To find the probability of both events occurring, we multiply the probabilities:

(3/12) * (4/12) = 12/144

Simplifying the fraction, we get:

12/144 = 1/12

Therefore, the probability that Abbey picks a black marker and then a purple marker, if she replaces the first marker, is 1/12.