Suppose a jar contains 16 red marbles and 36 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer as a reduced fraction.
The total number of marbles in the jar is 16 + 36 = 52.
To find the probability of pulling out 2 red marbles, we need to find the probability of pulling out one red marble and then another red marble.
The probability of the first marble being red is 16/52.
After pulling out 1 red marble, there are now 15 red marbles left in the jar, and the total number of marbles left is 51.
The probability of the second marble being red given that the first marble was red is 15/51.
To find the probability of both marbles being red, we multiply the probabilities of each event together: (16/52) * (15/51).
Reducing the fraction, we get:
16/52 * 15/51 = (4/13) * (5/17) = 20/221.
Therefore, the probability that both marbles are red is 20/221. Answer: \boxed{\frac{20}{221}}.