How to solve this probability problem You have three cards o

How to solve this probability problem?

You have three cards, one red on both sides, the second blue on one side and red on the other, the third blue on both sides. While your eyes are closed, your friend picks one card at random and places it on a table without taking color into account. You open your eyes and see red. What is the probability that the other side of the card (the side that is face down) is red?

Solution

SEE THERE ARE TOTAL 3 CARDS

SO THE PROBABILITY TO BE PICKED BY THE FRIEND FOR EACH CARD IS 1/3

BUT WE HAVE OPEN AND EYES AND SEE THE READ COLOR

AND THERE ARE 2 CARDS WITH RED COLOR , ONE BOTH SIDE AND ONE ONLY ONE SIDE

SO THE PROBABILITY THAT THE CARD WILL BE RED TO THE OTHER SIDE ALSO WILL BE 1/2 = 0.5

AS WE HAVE 2 CARDS RED BUT ONLY ONE IS BOTH SIDE RED.

HENCE 0.5