A box contains 9 new light bulbs and 6 used light bulbs. Each light bulb is the same size and shape. Meredith will randomly select 2 light bulbs from the box without replacement. What is the probability Meredith will select a new light bulb and then a used light bulb?
First, we need to find the probability of selecting a new light bulb on the first draw. Since there are 9 new light bulbs and a total of 15 light bulbs in the box, the probability of selecting a new light bulb on the first draw is:
P(new) = 9/15 = 3/5
After the first draw, there will be 8 new light bulbs and 6 used light bulbs left in the box. So, the probability of selecting a used light bulb on the second draw, given that a new bulb was selected on the first draw, is:
P(used|new) = 6/14 = 3/7
Note that we have 14 light bulbs left in the box after the first draw, since one light bulb was already selected.
To find the probability of selecting a new bulb and then a used bulb, we need to multiply the two probabilities:
P(new and used) = P(new) x P(used|new)
P(new and used) = (3/5) x (3/7)
P(new and used) = 9/35
Therefore, the probability that Meredith will select a new light bulb and then a used light bulb is 9/35 or approximately 0.257.