Question:
Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday 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?
Answer:
Total number of days = 5.
So Shyam and Ekta may visit the shop in 5 ways
So total number of outcomes = 5*5 = 25.
1. They can reach on the same day in 5 ways, i.e. (Tuesday-Tuesday), (Wednesday-Wednesday), (Thursday-Thursday), (Friday-Friday) and (Saturday-Saturday)
So,
probability that both will visit the shop on the same day = 5/25 = 1/5.
2. They can reach on consecutive days in following 8 ways: (tuesday-wednesday), (wednesday- tuesday), (wednesday-thursday), (thursday- wednesday), (thursday- friday), (friday-thusday), (friday-saturday), (saturday-friday).
probability that both will visit the shop on the consecutive day = 8/25.
3. probability that both will visit the shop on the same day = 1/5
So probability that both will visit the shop on the different day =1 - 1/5 = 4/5
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