Question

In a non-leap year, what is the probability that the last day of the year starts with a ‘t’?

Answer 1

Calculate the probability of the given condition

$\mathbf{P}\mathbf{\left(}\mathbf{E}\mathbf{\right)}\mathbf{}\mathbf{=}\frac{\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{favourable}\mathbf{}\mathbf{events}}{\mathbf{Total}\mathbf{}\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{outcomes}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{[}\mathbf{E}\mathbf{=}\mathbf{Event}\mathbf{]}$

Here $\mathrm{E}=$Last day of the year starting with ‘t’.

Number of days starting with ‘t’ in a week $=2$ [Tuesday, Thursday].

Total Number of days in a week$=7$

$\Rightarrow$ $P\left(E\right)=\frac{2}{7}$

Hence, the probability that the last day of the year starts with a ‘t’ is $\frac{2}{7}$.