Two customers Shyam and Ekta visit a shop on Tuesday to Saturday during a week. The visit not visit made by the each customer is at random.
All possible outcomes are.
| Visit Made by Shyam |
Possible Visits Made by Ekta |
| Tuesday |
Tuesday, Wednesday, Thursday, Friday, Saturday. |
| Wednesday |
Tuesday, Wednesday, Thursday, Friday, Saturday. |
| Thursday |
Tuesday, Wednesday, Thursday, Friday, Saturday. |
| Friday |
Tuesday, Wednesday, Thursday, Friday, Saturday. |
| Saturday |
Tuesday, Wednesday, Thursday, Friday, Saturday. |
If Tuesday be (T) be Wednesday (W) and so Thursday (Th), Friday (F) and Saturday (S).
The all possible outcomes are :
(T, T), (T, W), (T, Th), (T, F), (T, S)
(W, T), (W, W), (W, Th), (W, F), (W, S)
(Th, T), (Th, W), (Th, Th), (Th, F), (Th, S)
(F, T), (F, W), (F, Th), (F, F), (F, S)
(S, T), (S, W), (S, Tb), (S, F), (S, S)
The total number of all possible outcomes = 25
(i) The favourable outcomes of the visit made by two customers on same day
= (T, T), (W, W), (Th, Th), (F, F), (S, S)
∴ The number of favourable outcomes = 5.
∴ The probability that the two customers visit the shop on same day
= \(\frac { 5 }{ 25 }\) = \(\frac { 1 }{ 5 }\)
⇒ P(A) = \(\frac { 1 }{ 5 }\)
(ii) The favourable outcomes of visiting two customer on two consecutive days
= (Shyam, Ekta) = (T, W), (W, Th), (Th, F), (F, S)
or (Ekta, Shyam) = (W, T), (Th, W), (F, Th), (S, F)
∴ The number of favourable outcomes = 8
∴ The probability that two customers made the visit to the shop on consecutive days = \(\frac { 8 }{ 25 }\)
(iii) The probability ‘not visit’ made by two customers P(\(\overline { A }\)) = 1 – P(A)
= 1 – \(\frac { 1 }{ 5 }\) = \(\frac { 4 }{ 5 }\)
