Question

Two customers are visiting a particular shop in the same wee (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

(i) Probability of same day = 1/6

(ii) Probability of different days =5/6

(iii) Probability of consecutive days = 5/18

Step-by-step explanation:

Possible outcomes are:

Monday/Monday; Mon/Tues; Mon/Wed; Mon/Thur; Mon/Fri; Mon/Sat;  

Tues/Mon; Tues/Tues; Tues/Wed; Tues/Thur; Tues/Fri; Tues/Sat;

Wed/Mon; Wed/Tues; Wed/Wed; Wed/Thur; Wed/Fri; Wed/Sat;

Thur/Mon; Thur/Tues; Thur/Wed; Thur/Thur; Thur/Fri; Thur/Sat;

Fri/Mon; Fri/Tues; Fri/Wed; Fri/Thur; Fri/Fri; Fri/Sat;

Sat/Mon; Sat/Tues; Sat/Wed; Sat/Thur; Sat/Fri; Sat/Sat;

Total outcomes = 36

(i) Same day.

Favorable outcome = 6

Probability of same day = 6/36 = 1/6

(ii) Probability of different days = 30/36 = 5/6

(iii) Probability of consecutive days = 10/36 = 5/18