Two friend are visiting a particular shop inthe same week (Monday to Friday ) .each is equally likely to visit the shop on any day .what is the probability that both will visit the shop on (i) the same day (ii) consicutive day (iii) different day
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Answer:
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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