Question

Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on:

(i) the same day?

(ii) different days?

(iii) consecutive days?

Answer 1

Total no. of days to visit the shop = 6 {Mon to Sat}

Total no. possible outcomes = 6×6 = 36

i.e. two customers can visit the shop in 36 ways

(i) E⟶ event of visiting shop on the same day.

No. of favourable outcomes = 6 which are (M, M) (T, T) (Th, Th) (F, F) (S, S)

Probability, P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes)

P(E) = 6/36 = 1/6

(ii) E⟶ event of visiting shop on the same day.

E⟶ event of visiting shop on the different days.

In above bit, we calculated P(E) as 1/6

We know that, P(E) + P(Bar E) = 1

P(Bar E) = 1 – P(E)

= 1−1/6 = 5/6

(iii) E⟶ event of visiting shop on c

No. of favourable outcomes = 5 which are (M, T) (T, W) (W, Th) (Th, F) (F, S)

P(E) = 5/36