Question

Thirty days are in September, April, June and November; the other months have thirty-one days (except February). A month is chosen at random. What is the probability that the chosen month has exactly three days less than the maximum of 31, that is, exactly 28 days?

• A. \(\frac{15}{16}\)
• B. 1
• C. \(\frac{3}{48}\)
• D. None of these

Hint:

Three days less than 31 is 28 days; only February has 28 days, so the probability is \(\frac{1}{12}\). Check whether this matches any listed fraction.

Answer 1

The Correct Option is D

This question is really asking: out of the 12 months of the year, how many have exactly 28 days, and what fraction is that? Three days less than the maximum of 31 days is $31 - 3 = 28$ days, and in an ordinary calendar year only February has 28 days. So the true probability is $\frac{1}{12}$. Now check each option against this value.

1. \(\frac{15}{16}\): this equals $0.9375$, almost a certainty. That would mean nearly every month has 28 days, which is false, so this option is wrong.
2. 1: this would mean every single month has 28 days, which is obviously false since most months have 30 or 31 days.
3. \(\frac{3}{48}\): this simplifies to $\frac{1}{16} = 0.0625$. It looks close to $\frac{1}{12} \approx 0.0833$ but the two fractions are not equal, since $1/12 \neq 1/16$.
4. None of these: since the correct probability $\frac{1}{12}$ does not equal any of the first three fractions, this is the only option left standing.

Because $\frac{1}{12}$ cannot be written as $\frac{15}{16}$, as $1$, or as $\frac{3}{48}$, the only option that can be correct is "None of these".

Let's summarize:

• Only February has 28 days out of the 12 months, giving a probability of $\frac{1}{12}$.
• $\frac{3}{48}$ reduces to $\frac{1}{16}$, a different fraction from $\frac{1}{12}$, so it is a near-miss distractor, not the answer.

The correct probability, $\frac{1}{12}$, is not among the first three choices, so the answer is "None of these".