A box contains 3 pens, 2 markers, and 1 highlighter.

Question

Tara selects one item at random and does not return it to the box. She then selects a second item at random. What is the probability that Tara selects 1 pen and then 1 marker?

A. 27/30

B. 6/36

C. 6/30

D. 5/36

Answer 1

We have 2 sequential events that must each happen (dependent), and we want the probability of a specific outcome to both of those events.

(1) First, we take the probability of the first event which is selecting 1 pen. We have 3 pens and 6 total items in the box. This means we have 3 opportunities to select a pen from 6 items. We can represent this probability as a fraction: 3/6

(2) Second, we must then select a marker after having selected a pen. There are 2 markers in the box, but we now only have 5 items in the box since a pen has already been removed in the first step. We can represent this probability as a fraction: 2/5

Since both events are dependent (they both must happen to satisfy the problem) we will multiply their probabilities.

3/6 x 2/5 = 6/30 which is C from the list of choices. This can be further simplified to 1/5 or 20%.