A bag contains three red marbles and three blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. Find the probability both marbles are red.

Answer 1

Let, A be the event denoting the first marble to be red and B be the event denoting the second marble to be red.

Pr(1^st marble to be red) = P(A) = 3/6 = 1/2

After A has happened, there are 5 marbles in the bag (2 red + 3 blue).

Pr(2^nd marble to be red | 1^st marble to be red) = P(B | A) = 2/5

Pr(A∩B) = P(B | A) × P(A) = 2/5 × 1/2 = 1/5