Question

There are three cards. One is green on both sides, the second is red on both sides and the third is red on one side and green on the other. We choose a card at random and we see one side (also chosen at random). If the side we see is green, what is the probability that the other side is also green? Many people intuitively answer 1/2 but this is not the correct answer. (Hint: Label one side of each card as 1 and the other as 2. An outcome is then $(x,y)$ where $x$ is the color and $y$ is the side of the card we see.)

Answer 1

Explanation:

Given that there are three cards. One is green on both sides, the second is red on both sides and the third is red on one side and green on the other. We choose a card at random and we see one side (also chosen at random)

If (x,y) is the random variable representing the colours of cards then

(x,y) can take values as (g,g) (r,r) or (r,g)

(Assume that (r,g) is equivalent to (g,r))

B= chosen card at random shows green (g,g) or (r,g)

A = Chosen card other side also as green or chosen card is (g,g)

P(AB) = 1/3

P(B) = 2/3

Hence P(A/B) = P(AB)/P(B) = 1/2

1/2 is only the correct answer.