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 1

i) Possibility of visiting the shop on same day $=\left\{\right(tue,tue),(wed,wed),(thurs,thurs),(fri,fri),(sat,sat\left)\right\}$

Total outcomes is $5\times 5=25$

P(on the same day) $=\frac{5}{25}=\frac{1}{5}$

ii) Possibility of visiting the shop on consecutive days $=\left\{\right(tue,wed),(wed,thurs),(thurs,fri),(fri,sat),(thurs,wed),(fri,thurs),(sat,fri),(wed,tue\left)\right\}$

Total outcomes is $25.$

P(on consecutive days) $=\frac{8}{25}$

iii) Possibility of visiting the shop on different days $=\{tue,wed,thurs,fri,sat\}$

P(on different days) $=1-$ P(on same day) $=1-\frac{1}{5}=\frac{4}{5}$