The probability of a non-leap year selected at random will contain 53 Sundays is

Whenever a period of time spans a whole number of complete weeks plus a few extra ('odd') days, each of the 7 weekdays is equally likely to be one of those extra days. So, for a period with k extra days, the probability that a particular weekday (such as Sunday) falls among the extra days is k/7.

1. A non-leap year has 365 days; dividing by 7 gives 52 complete weeks with a remainder of 1 day, so k = 1 extra day here.

2. The 52 complete weeks alone already contribute exactly 52 Sundays (and 52 of every other weekday).

3. For the year to have 53 Sundays, this single extra day must itself be a Sunday.

4. Applying the general rule with k = 1 extra day gives the probability 1/7.

Since exactly one extra day exists here, only one of the seven equally likely weekdays is favourable, giving a single well-defined probability that matches one of the listed fractions - not several at once, and not an unlisted value. (Note that k = 2 extra days, as in a leap year, would instead give 2/7.) Hence the required probability is 1/7.