Question

The probability that the month of April has exactly 5 Mondays is _________.

Answer 1

Number of days in the month of April = 30

There are four complete weeks in the month of April. There are two more extra days in month of April.

The remaining two 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 cases = 7

Let E be the event that the month of April has exactly 5 Mondays. Now, the event E can occur if the two extra days are either Sunday and Monday or Monday and Tuesday.

Favourable number of cases = 2

∴ Probability that the month of April has exactly 5 Mondays = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{cases}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{cases}}=\frac{2}{7}$

The probability that the month of April has exactly 5 Mondays is $\underline{\frac{2}{7}}$.