You have a bag which contains 15 slips of paper that are num - bered 1 through 15. You pull a piece of paper from the bag, do not return it, and then pull another piece of paper from the bag. What is the probability that both slips of paper you pull are out are a multiple of 4? Express your answer as a fully simplified fraction.

The correct answer is 1/35 (fully simplified fraction)

Step-by-step explanation:

Number of slips of paper in the bag = 15

Number of slips of paper in the bag that are a multiple of 4 = 3 (those numbered 4, 8 and 12)

Using Laplace Rule, that states that the probability of an event X is obtained by dividing the number of results that form event X by the number of possible outcomes, provided that the elementary events are equiprobable, that is, that all possible outcomes have the same probability.

Probability of pulling a 1st piece of paper multiple of 4 = 3/15 = 1/5

Now we have a second event Y that is not independent from the first event X, because now the number of slips is 14 and not 15, you're not returning the first slip of paper.

Probability of pulling a 2nd piece of paper multiple of 4 = Probability of the 1st event * probability of the 2nd event after it happened the 1st one

Probability of pulling a 2nd piece of paper multiple of 4 = 1/5 * 2/14

Probability of pulling a 2nd piece of paper multiple of 4 = 2/70 = 1/35

The probability of pulling two slips of paper both numbered with a multiple of 4 is 1/35.