On a standard six-sided die, which is the probability of rolling an odd number?

• A. 1/4
• B. 1/6
• C. 1/2
• D. 1

Answer: (C)

Probability is the ratio of favorable outcomes to the total number of outcomes when each outcome is equally likely. A standard die has six faces, and the odd faces are 1, 3, and 5—three favorable outcomes. So the probability of rolling an odd number is 3 out of 6, which simplifies to 1/2. In other words, about half the rolls should be odd over the long run.

The other fractions don’t fit because they don’t match three favorable outcomes out of six total: 1/4 would imply 1.5 favorable outcomes (not possible), 1/6 would imply only one favorable outcome, and 1 would imply always getting an odd number, which isn’t true.