(Q1) 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

(i) the same day?

(ii) consecutive days?

(iii) different days?

Answer :

Shyam and Ekta can visit the shop in the following combination:

(T Tu) (W, Tu) (Th, Tu) (F, Tu) (S, Tu) (Tu, W) (W, W) (Th, W) (F, W) (S, W) (Tu, Th) (W, Th)
(Th, F) (F, Th) (S, Th) (Tu, F) (W, F) (Th, S) (F, F) (S, F) (Tu, S) (W, S) (Th, Th) (F, S) (S, S)

∴ Number of total outcomes = 5 × 5 = 5² = [also from the above table]

(i) Number of favourable outcomes to that of visiting on the same day =

(ii) Number of outcomes favourable to consecutive days =

∴ Probability of visiting the shop on consecutive days =

(iii) If P(E) is the probability of visiting the shop on the same day,then P(Ē) is the probability of visiting the shop not on the same day.

i.e., P(Ē) is the probability of visiting the shop on different days.

Such that P(E) + P(Ē) = 1