Suppose a jar contains 19 red marbles and 10 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

Let R be the event that you pull out a red marble and B be the event that you pull out a blue marble.

P(R₁) = 19/29

P(R₂) = 18/28

P(R₁ ∩ R₂) = P(R₁)*P(R₂) = (19/29)*(18/28) = 342/812 = 0.4212

The probability of pulling out 2 red marbles from the bag without replacement is 0.4212.