Two customers are visiting a particular shop in the same week (monday 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?
Answers
Answer:
(i) 1/5 (ii) 5/36 (iii)5/6
Step-by-step explanation:
Total number of days = 6
They are : Mon, Tues, Wed, Thurs, Fri, Sat
Total number of possible combinations = 6 x 6 = 36
They are:
(Mon, Mon), (Mon, Tues) (Mon, Wed) .... (Mon, Sat)
(Tues, Mon), (Tues, Tues) (Tues, Wed) .... (Tues, Sat)
....
(Sat, Mon), (Sat, Tues) (Sat, Wed) .... (Sat, Sat)
Question (i)
Total number of days that they will visit on the same day = 6
They are:
(Mon, Mon), (Tues, Tues), (Wed, Wed), (Thurs, Thurs), (Fri, Fri), (Sat, Sat)
P(two customers visit on the same day) = 6/36 = 1/6
Question (ii)
Total number of days that can be consecutive = 5
They are:
(Mon, Tues), (Tues, Wed), (Wed, Thurs), (Thurs, Fri), (Fri, Sat)
P(two customers visit on the same day) = 5/36
Question (iii)
Total number of different days = Total days - Total same day
Total number of different days = 36 - 6 = 30
P(Two customers visit on different day = 30/36 = 5/6
Answer: (i) 1/5 (ii) 5/36 (iii)5/6
Answer:
i) 1/6 ii)5/18 iii)5/6
Step-by-step explanation:
No of customers = 2
Possible sample space of one customer visit={monday,tuesday,wednesday,thursday,friday,saturday}
n(A)=6
For the second customer possible visit days = {monday,tuesday,wednesday,thursday,friday,saturday}
n(B)=6
Total sample space by law of probability = n(A)*n(B)
=6*6 = 36
1) If the visit same day
possible events outcomes are both on the same day
so n(E) = 6
Probability = n(E) / Total sample space
= 6/ 36
=1/6
2) Consecutive days
the sample space would be
if one visits on monday then other visit on tuesday
if one visit on tuesday other visit on wednesday
if one visit on wednesday other visit on thursday
if one visit on thursday other visit on friday
and vice versa
so n(E) for first = 5 and for the other person = 5
so total will be = 10
probability = n(E) / total
= 10 / 36
=5/18
iii) probability of same days = 1/6
probability of different days = 1 - probability of same days
= 1- 1/6
=5/6