In a non-leap year, what is the probability that the last day of the year…
2023
In a non-leap year, what is the probability that the last day of the year starts with the letter 'T'?
- A.
3/7
- B.
2/7
- C.
1/9
- D.
2/8
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept: A non-leap year has 365 days, i.e. 52 complete weeks + 1 extra day. Since 364 = 52 x 7, the weekday of the year's 1st day and its 365th (last) day are always the same. When the year's starting weekday is not fixed by the question, this last day is equally likely to be any of the 7 weekdays — a uniform sample space of size 7.
Application: Among the 7 weekdays — Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday — only Tuesday and Thursday begin with the letter 'T'. So the number of favourable outcomes is 2, out of the 7 equally likely outcomes for the last day of the year.
Cross-check: listing all 7 weekdays confirms exactly two start with 'T'.
Sunday - does not start with T
Monday - does not start with T
Tuesday - starts with T (favourable)
Wednesday - does not start with T
Thursday - starts with T (favourable)
Friday - does not start with T
Saturday - does not start with T
Answer: Probability = 2/7.