A box contains three cards One card is red on both sides one

A box contains three cards. One card is red on both sides, one card is green on both sides, and one card is red on one side and green on the other. One card is selected from the box at random, and the color on one side is observed. If this side is green, what is the probability that the other side of the card is also green?

Solution

As one side is green, that it must be that it is the second or third card. The probability of getting each is is 1/2, as we just have 2 options now.

Now,

P(other side is green|one side is green) = P(second card) P(other side is green|second card) +
P(other side is green|one side is green) = P(third card) P(other side is green|third card)

= (1/2)*(1) + (1/2)(1/2)

= 3/4 or 0.75 [ANSWER]