No homework help here...just curious as to what range of answers I'll get.
There are three cards in a hat. One is red on both sides, one is white on both sides, and one is red on one side and white on the other side. You close your eyes, pull a card from the hat, and set it on the table. The side facing up is red. What is the probability that the other side is also red?
(No...it is not 1/2.)
There are three cards in a hat. One is red on both sides, one is white on both sides, and one is red on one side and white on the other side. You close your eyes, pull a card from the hat, and set it on the table. The side facing up is red. What is the probability that the other side is also red?
(No...it is not 1/2.)
-
P[draw "double red" card & upper side red] = 1/3 * 1 = 1/3
P[draw "single red" card & upper side is red] = 1/3 * 1/2 = 1/6
P[upper side red] = 1/3 + 1/6 = 1/2
P[other side red] = [1/3] / [ 1/2] = 2/3 <--------
P[draw "single red" card & upper side is red] = 1/3 * 1/2 = 1/6
P[upper side red] = 1/3 + 1/6 = 1/2
P[other side red] = [1/3] / [ 1/2] = 2/3 <--------