Question

Suppose we have three cards. One is colored red on both sides, one is black on both sides, and one is red on one side and black on the other. We place these three cards in a hat and shuffle them. We draw one card and place in on the table, so only one side is visible. If that side is red, what is the probability that it’s the red-black card?

Answer 1

Answer:

Given,

To determine the probability that it’s the red-black card

P(one side is red) = P(red black card)*P(one side red|red black card) + P(red red card)*P(one side red|red red card) + P(black black card)*P(one side red|black black card)

substitute known values

= (1/3)*(1/2) + (1/3)*(1) + (1/3)*0

= 1/6 + 1/3 + 0

= 1/2

Now consider,

P(Red-black card given one side is red) = P(red black card)*P(one side red|red black card) / P(one side is red)

substitute values

= (1/3)*(1/2) / (1/2)

= 1/3

= 0.33