# Two customers are visiting a particular shop in the same week

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?

Solution:

GIVEN: 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.

TO FIND: Probability that both will visit the shop on:

(i) The same day

(ii) Different days

(iii) Consecutive days

Two customers can visit the shop on two days in ways.

Hence total number of ways =36

(i) Two customer can visit the shop on any day of the week i.e.

MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY

Favorable number of ways = 6

We know that PROBABILITY =

Hence probability of the customer visiting the shop on the same day =

(ii) We know that sum of probability of occurrence of an event and probability of non occurrence of an event is 1.

$P(\mathrm{E})+P(\overline{\mathrm{E}})=1$

$\frac{1}{6}+\mathrm{P}(\overline{\mathrm{E}})=1$

$P(\bar{E})=1-\frac{1}{6}$

Hence probability of the customer visiting the shop on the different day is

(iii) Two costumer can visit the shop in two consecutive days in the following ways:

(MONDAY, TUESDAY), (WEDNESDAY, THURSDAY), (THURSDAY, FRIDAY) (FRIDAY, SATURDAY)

Favorable number of ways =5

We know that PROBABILITY =

Hence probability of the customer visiting the shop on two consecutive days =