Question

Thirty days are in September, April, June and November. Some months are of thirty one days. A month is chosen at random. Then its probability of having exactly three days less than maximum of 31 is

• A. \(\frac{15}{16}\)
• B. 1
• C. \(\frac{03}{48}\)
• D. None of these

Answer 1

The Correct Option is D

To find the probability that a chosen month has exactly three days less than the maximum of 31 days, we need to first identify which months have 30 days and which months have 31 days. According to the rhyme, "Thirty days hath September, April, June, and November." This means these four months have 30 days.

Other months have 31 days except for February, which has 28 or 29 days but is irrelevant in this context because we are only considering months that are either 30 or 31 days long.

The total number of months in a year is 12.

Month	Days
January	31
February	28/29
March	31
April	30
May	31
June	30
July	31
August	31
September	30
October	31
November	30
December	31

From the table, there are 4 months with 30 days (April, June, September, November). These months have exactly three days less than the maximum of 31 days.

Thus, the probability that a month chosen at random is one with 30 days is calculated as follows:

\[ P(\text{30-day month}) = \frac{\text{Number of 30-day months}}{\text{Total months}} = \frac{4}{12} = \frac{1}{3} \]

None of the options given match this probability, so the correct answer is: None of these.