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?
Since there are 5 days and both can go to the shop in 5 ways each so,
The total number of possible outcomes = 5 × 5 = 25
(i) The number of favourable events = 5 (Tue., Tue.), (Wed., Wed.), (Thu., Thu.), (Fri., Fri.), (Sat., Sat.)
P (both visiting on the same day) = \(\frac{5}{25}\) = \(\frac{1}{5}\)
(ii) The number of favourable events = 8 (Tue., Wed.), (Wed., Thu.), (Thu., Fri.), (Fri., Sat.), (Sat., Fri.), (Fri., Thu.), (Thu., Wed.), and (Wed., Tue.)
P(both visiting on the consecutive days) = \(\frac{8}{25}\)
(iii) P (both visiting on the different days) = 1-P (both visiting on the same day)
So, P (both visiting on the different days) = 1 - \(\frac{1}{5}\) = \(\frac{4}{5}\)