Question

Suppose you have 3 cards:

1. A red card is red on both sides.

2. A blue card is blue on both sides.

3. A mixed card is red on one side and blue on the other.

You gather the cards and toss them into a hat. You then select one randomly from the hat and place it on the table. Given that the side facing up is blue, what is the probability that the other side is also a blue?

		1/2
		1/4
		2/3
		1/3

Answer 1

Total cards = 3

Total sides = 6

Probability of side facing up is blue, P(B1) = 3/6 = 1/2

Probability that both sides are blue, P( B1 and B2) = 1/3

Probability of second side being blue, given that first side is blue, P(B2| B1) = P(B1 nd B2)/ P(B1)

$= \frac{(1/3)}{(1/2)} = \frac{\textbf{2}}{\textbf{3}}$