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 different days?

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Solution

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:
(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)
$∴$ Total number of outcomes = 25
Number of favourable outcomes of visiting on different days are 25 - 5 = 20
$∴$ Number of favourable outcomes = 20
Hence, required probability = $\frac{20}{25} = \frac{4}{5}$

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