Question

Find the probability that a leap year selected at random will contain $53$ Tuesdays.

• A. $\frac{2}{7}$
• B. $\frac{5}{7}$
• C. $\frac{4}{7}$
• D. $\frac{3}{7}$

Answer 1

The correct option is A $\frac{2}{7}$

In a leap year there are $366$ days
We have, $366$ days $=52$ weeks and $2$ days.

Thus, a leap year will have $52$ Tuesdays.

The remaining $2$ days can be
(i) Sunday and Monday
(ii) Monday and Tuesday
(iii) Tuesday and Wednesday
(iv) Wednesday and Thursday
(v) Thursday and Friday
(vi) Friday and Saturday
(vii) Saturday and Sunday

Total number of possible cases $=7$
Total number of favourable cases $=2$
Hence, required probability = $\frac{2}{7}$