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) different days (iii) consecutive day ?

Explanation

(i) Both the customers visit the shop on the same day, i.e., there. are 6 days (Monday to Saturday) and each is equally likely.
`therefore` Probability of both will visit on the same day
= First will go on Monday and the other will also go on Monday or first will go on Tuesday and other will go on Tuesday
:
or first will go on Saturday and other will also go on Saturday
`=(1)/(6)xx(1)/(6)+(1)/(6)xx(1)/(6)+...+(1)/(6)xx(1)/(6)=6xx(1)/(6)xx(1)/(6)=(1)/(6)`
Alternative Method:
First person will definitely go to the market on any of the six days with probability 1 (sure event). If both go to the market same day then second person has only 1 choice (only that 1 day when first goes). So, its probability of going to the market `=(1)/(6).`
`therefore" Required probability "=1xx(1)/(6)=(1)/(6)`
(ii) First person will definitely go to the market on any of the six days with probability 1 (sure event). Since, both will not go on the same day, so second person has now only 5 choices (except this 1 day when first go to the market). So, the probability of second
man go to the other day `=(5)/(6).`
`therefore" Required probability "=1xx(5)/(6)=(5)/(6)`
(iii) There are 5 consecutive days, i.e., Monday Tuesday, Tuesday Wednesday, Wednesday Thursday, Thursday Friday, Friday Saturday.
`therefore" Required probability "=5xx(1)/(6)xx(1)/(6)=(5)/(36)`