Question

What is the probability of-

i) Sundays in a leap year

ii) sundays in a non-leap year

Answer 1

$$\begin{gathered} \mathrm{(i)\; A}\mathrm{leap}\mathrm{year}\mathrm{has}366\mathrm{days,}t\mathrm{herefore}52\mathrm{weeks}\mathrm{i.e.}52\mathrm{Sunday}\mathrm{and}2\mathrm{days.}\mathrm{The}\mathrm{remaining}2\mathrm{days}\mathrm{may}\mathrm{be}\mathrm{any}\mathrm{of}\mathrm{the}\mathrm{following\; :} \\ (iSundayand\hspace{0.17em}Monday \\ \left(ii\right)MondayandTuesday \\ \left(iii\right)TuesdayandWednesday \\ \left(iv\right)WednesdayandThursday \\ \left(v\right)ThursdayandFriday \\ \left(vi\right)FridayandSaturday \\ \left(vii\right)SaturadyandSunday \\ Forhaving53sundaysinayear,oneoftheremaining2daysmustbeaSunday. \\ n\left(S\right)=\mathrm{}7 \\ n\left(E\right)=\mathrm{}2 \\ P\left(E\right)=n\left(E\right)/n\left(S\right)=2/7 \end{gathered}$$