Question

In the whiteboard tray, there are 20 whiteboard pens. Among the pens, 5 are dry/out of ink. The professor picks up tyy distinct pens. State answers as a reduced fraction. What is the probability that both are dry/out of ink? 5/20⋅ 5/20

=1/16 b. What is the probability that one pen is dry/out of ink but the other writes well? 5/20⋅ 15/20
=3/16 Workspace ↓

Answer 1

To find the probability that both pens are dry/out of ink, multiply the probabilities of each event happening. To find the probability that one pen is dry/out of ink but the other writes well, multiply the appropriate probabilities together.

Step-by-step explanation:

To find the probability that both pens are dry/out of ink, we need to multiply the probability of selecting a dry pen on the first draw with the probability of selecting another dry pen on the second draw. The probability of selecting a dry pen on the first draw is 5/20, and since we are not replacing the pen, the probability of selecting a dry pen on the second draw is 4/19. Therefore, the probability that both pens are dry/out of ink is (5/20) * (4/19) = 1/19.

To find the probability that one pen is dry/out of ink but the other writes well, we need to multiply the probability of selecting a dry pen on the first draw with the probability of selecting a pen that writes well on the second draw. The probability of selecting a dry pen on the first draw is 5/20, and since we are not replacing the pen, the probability of selecting a pen that writes well on the second draw is 15/19. Therefore, the probability that one pen is dry/out of ink but the other writes well is (5/20) * (15/19) = 15/76.