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?
$(i)$ the same day?
$(ii)$ consecutive days?
$(iii)$ different days?
(A) There are a total of $5$ days (Tuesday,Wednesday,Thursday,Friday,Saturday). Shyam can visit the shop in $5$ ways and Ekta can visit the shop in $5$ ways.
Therefore,total number of outcomes $= 5 \times 5 = 25$.
$(i)$ They can reach on the same day in $5$ ways: $(T, T), (W, W), (Th, Th), (F, F), (S, S)$.
$P(\text{same day}) = \frac{5}{25} = \frac{1}{5}$.
$(ii)$ They can reach on consecutive days in $8$ ways: $(T, W), (W, Th), (Th, F), (F, S), (W, T), (Th, W), (F, Th), (S, F)$.
$P(\text{consecutive days}) = \frac{8}{25}$.
$(iii)$ $P(\text{different days}) = 1 - P(\text{same day}) = 1 - \frac{1}{5} = \frac{4}{5}$.
Therefore,total number of outcomes $= 5 \times 5 = 25$.
$(i)$ They can reach on the same day in $5$ ways: $(T, T), (W, W), (Th, Th), (F, F), (S, S)$.
$P(\text{same day}) = \frac{5}{25} = \frac{1}{5}$.
$(ii)$ They can reach on consecutive days in $8$ ways: $(T, W), (W, Th), (Th, F), (F, S), (W, T), (Th, W), (F, Th), (S, F)$.
$P(\text{consecutive days}) = \frac{8}{25}$.
$(iii)$ $P(\text{different days}) = 1 - P(\text{same day}) = 1 - \frac{1}{5} = \frac{4}{5}$.
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