Question

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the same day?

Answer 1

Total favourable outcomes associated to the random experiment of visiting a particular shop in the same week (Tuesday to Saturday) by two customers Shyam and Ekta are:
(Here : T- Tuesday, W- wednesday, Th- Thrusday, F- Friday, S- saturday)
(T,T) (T,W) (T,TH) (T,F) (T,S)
(W,T) (W,W) (W,TH) (W,F) (W,S)
(TH,T) (TH,W) (TH,TH) (TH,F) (TH,S)
(F,T) (F,W) (F,TH) (F,F) (F,S)
(S,T) (S,W) (S,TH) (S,F) (S,S)
$\therefore$ Total number of favourable outcomes = 25

The favourable outcomes of visiting on the same day are ( T, T) (W,W) (TH,TH) (F,F) and (S,S).
$\therefore$ Number of favourable outcomes = 5
Hence, required probability = $\frac{favourableoutcome}{totalpossibleoutcome}=\frac{5}{25}=\frac{1}{5}$