Question

There are 10 rolls of film in a box and 3 are defective. Two rolls are to be selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?

a) 1/2, or 0.50
b) 1/4, or 0.25
c) 1/120, or about 0.0083
d) 1/15, or about 0.07

Answer 1

The probability of selecting a defective roll followed by another defective roll can be calculated by multiplying the probabilities of the two events. In this case, the probability is 1/15, or approximately 0.07. The correct answer is D.

Step-by-step explanation:

In this problem, we are choosing two rolls without replacement from a box containing 10 rolls, 3 of which are defective. The probability of selecting a defective roll followed by another defective roll can be calculated as follows:

1. First, we select one defective roll from the 3 in the box. The probability of selecting a defective roll is 3/10.
2. After the first roll is selected, there are 9 rolls left in the box, and 2 of them are defective. So the probability of selecting a second defective roll from the remaining 9 rolls is 2/9.
3. Since the rolls are selected without replacement, we multiply the probabilities of the two events to find the overall probability. So, the probability of selecting a defective roll followed by another defective roll is (3/10) * (2/9) = 6/90 = 1/15, or approximately 0.07 (option d).