Two customers are visiting a particular …

Total number of days to visit the shop = 6
Two customers can visit the shop on two days in 6 {tex}\times{/tex} 6 = 36 ways
So total number of outcomes = 36

1. Two customers can visit the shop on same day of the week in 6 ways i.e.
   (M, M), (T, T), (W, W), (Th, Th), (F, F), (S, S)
   Favourable number of ways = 6
   {tex}\therefore{/tex}P(both will reach on same day) = {tex}\frac{6}{36}{/tex}={tex}\frac{1}{6}{/tex}
2. Two customers can visit the shop on consecutive days in 5 ways i.e.
   (M, T), (T, W), (W, Th), (Th, F), (F, S)
   Favourable number of ways = 5
   P(both will reach on consecutive days) = {tex}\frac{5}{36}{/tex}.
3. We know, Probability of occurrence of an event  +  Probability of non occurrence of event  = 1
   i.e. P(E) + {tex}P ( \overline { E } ){/tex} = 1
   P(both will reach on same day) = {tex}\frac{1}{6}{/tex}
   {tex}\Rightarrow{/tex} {tex}\frac{1}{6}{/tex} + {tex}P ( \overline { E } ){/tex} = 1 
   {tex}\Rightarrow{/tex} {tex}P ( \overline { E } ){/tex}= 1 - {tex}\frac{1}{6}{/tex}
   {tex}\Rightarrow{/tex} {tex}P ( \overline { E } ){/tex} = {tex}\frac{5}{6}{/tex}
   Hence, P(both will reach on different day) = {tex}\frac{5}{6}{/tex}