Question

Suppose a jar contains 10 red marbles and 13 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.

Answer 1

Number of red marbles = 10

Total number of marbles = 10+13 = 23

Number of ways 2 marbles are drawn from the jar = 23C2 = 253 (here C is combination)

Number of ways 2 red marbles are drawn from the jar = 10C2 = 45

If 2 marbles were drawn from the jar then probability that both are red = (Number of ways 2 red marbles are drawn from the jar Number of ways 2 marbles are drawn from the jar)

If 2 marbles were drawn from the jar then probability that both are red = (45 253) = 0.1779

Answer: The probability that both are red is 0.1779