There are three cards in a box. Both sides of one card are black, both sides…
2016
There are three cards in a box. Both sides of one card are black, both sides of one card are red, and the third card has one black side and one red side. We pick a card at random and observe only one side.
What is the probability that the opposite side is the same colour as the one side we observed ?
- A.
3/4
- B.
2/3
- C.
1/2
- D.
1/3
Attempted by 65 students.
Show answer & explanation
Correct answer: B
Answer: 2/3
Explanation by counting faces:
List the cards and their faces: one card has two black faces, one has two red faces, and one has one black and one red face. That gives 6 faces in total.
Count faces whose opposite side is the same colour: the two black faces on the double-black card both have black on the opposite side (2), and the two red faces on the double-red card both have red on the opposite side (2). The mixed card's faces have opposite colours, so contribute 0.
So there are 4 favourable faces out of 6 total faces, giving probability 4/6 = 2/3.
Alternative conditional view: if you observe a black face, there are 3 black faces in total and 2 of them come from the double-black card, so the chance the opposite is black is 2/3 (and similarly for observing red).