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?

Please show work, and explain reasoning behind your answer

Solution

Let\'s suppose the three cards are C1(with both sides green), C2(with one side green and another red) and C3(both sides are red). Each has two sides (mark A and B)

Now, condition is that the card selected has one side green. So, probability of C3 selection is 0.

Now, Collect the total cases with one side green:

And, favourable cases (other side should be green too) are:

so, probability is: 2 / 3