Question

An envelope contains three cards: a black card that is black on both sides, a white card that is white on both sides, and a mixed card that is black on one side and white on the other. You select one card at random and note that the side facing up is black. What is the probability that the other side is also black?

Answer 1

There is a 2/3 probability that the other side is also black.

Explanation:

Here let B1: Event of picking a card that has a black side

B2: Event of picking a card that has BOTH black side.

Now, by the CONDITIONAL PROBABILITY:

`P(B_2/B_1 ) = (P(B_1\cap B_2))/(P(B_1))`

Now, as EXACTLY ONE CARD has both sides BLACK in three cards.

⇒ P (B1 ∩ B2) = 1 /3

Also, Out if total 6 sides of cards, 3 are BLACK from one side.

⇒ P (B1 ) = 3 /6 = 1/2

Putting these values in the formula, we get:

`P(B_2/B_1 ) = (P(B_1\cap B_2))/(P(B_1)) = (1)/(3) *(2)/(1) = (2)/(3)`

⇒ P (B2 / B1) = 2/3

Hence, there is a 2/3 probability that the other side is also black.