1973 AMC 12 Problem 23

Question

There are two cards; one is red on both sides and the other is red on one side and blue on the other. The cards have the same probability

(\frac{1}{2})

of being chosen, and one is chosen and placed on the table. If the upper side of the card on the table is red, then the probability that the under-side is also red is

\dfrac14

\dfrac13

\dfrac12

\dfrac23

\dfrac34

Answer: D

Concepts:conditional probability basic probability

Difficulty rating: 1670

Small hint:

Condition on the individual card sides that could be showing red

Big hint:

There are three equally likely visible red faces; determine the color behind each

Solution:

Among outcomes having a red upper side, either of the two red faces of the red-red card or the red face of the red-blue card can be uppermost. These three visible red faces are equally likely. The underside is red in the first two cases and blue in the third, so the conditional probability is

\frac23.

Therefore, the correct answer is D.