A deck contains 4 cards where both sides are of the same col

A deck contains 4 cards where both sides are of the same color, 5 cards where both side are of the same color blue AND 3 cards where both colors. Yellow and blue are on each side of the cards. If one of the cards selected from the deck what is the probability that the chosen side is blue?

Solution

Let

Y = the card is both yellow
B = the card is both blue
M = the card is a mixture of blue and yellow
FB = the face chosen is blue

Thus,

P(FB) = P(Y) P(FB|Y) + P(B) P(FB|B) + P(M) P(FB|M)

= (4/12)*(0) + (5/12)*(1) + (3/12)*(1/2) = 0.541666667 [ANSWER]