Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday).

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?

Solution:

There are a total of 5 days. Shyam can go to the shop in 5 ways and Ekta can go to the shop in 5 ways.

Therefore, total number of outcomes = 5 × 5 = 25

(i) They can reach on the same day in 5 ways.

i.e., (t, t), (w, w), (th, th), (f, f), (s, s)

$\mathrm{P}($ both will reach on same day $)=\frac{5}{25}=\frac{1}{5}$

(ii) They can reach on consecutive days in these 8 ways - (t, w), (w, th), (th, f), (f, s), (w, t), (th, w), (f, th), (s, f).

Therefore, $P$ (both will reach on consecutive days) $=\frac{8}{25}$

(iii) $P$ (both will reach on same day) $=\frac{1}{5}[($ From (i) $]$

$P$ (both will reach on different days) $=1-\frac{1}{5}=\frac{4}{5}$