Two customers are visiting a particular shop in the same week (monday to saturday) Each is equally likely to - Maths - Probability

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 the other what is the probability that both will
visit the shop on the
i)same day
ii)different day
iii)consecutive days

Manish Bharti · Accepted Answer

Total number of days = 6
first customer can visit any day (between monday to saturday)i.e. 6 days
second customer can also visit any day (between monday to saturday)i.e. 6 days
therefore total number of ways to visit the shop by two customers = 6×6=36 ways

1.
if they visit the shop same day.
so number of ways to visit the shop on the same day is 6 ( any day between Monday and Saturday)
Required probability= $\frac{6}{36} = \frac{1}{6}$

2.
Probability of visiting the shop on different day = 1 - probability of visiting the shop on same day
$= 1 - \frac{1}{6} = \frac{5}{6}$

3.. if they visit the shop on consecutive day, following cases are possible
Monday Tuesday
Tuesday Wednesday
Wednesday Thursday
Thursday Friday
Friday Saturday
so we have 5 pair of days, in which they can visit. since there are 2 different customers, it can be done in 2 ways.
so total no of ways when they can visit in consecutive days =5×2=10

hence the required probability = $\frac{10}{36} = \frac{5}{18}$

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 the other. what is the probability that both will visit the shop on the i)same day ii)different day iii)consecutive days

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 the other. what is the probability that both will visit the shop on the

i)same day

ii)different day

iii)consecutive days