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# 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?

Given:

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

Each is equally likely to visit the shop on any one day as on another.

To do:

We have to find the probability that both will visit the shop on

(i) the same day

(ii) consecutive

days

(iii) different days

Solution:

Number of days from Tuesday to Saturday $=5$

This implies,

The total number of possible outcomes $n=5\times5=25$.

(i) Number of outcomes where both visit the shop on the same day $=5$

Total number of favourable outcomes $=5$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that both will visit the shop on the same day $=\frac{5}{25}$

$=\frac{1}{5}$

The probability that both will visit the shop on the same day is $\frac{1}{5}$.

(ii) Number of outcomes where both visit the shop on consecutive days $=4+4=8$

Total number of favourable outcomes $=8$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that both will visit the shop on consecutive days $=\frac{8}{25}$

The probability that both will visit the shop on consecutive days is $\frac{8}{25}$.

(iii) Number of outcomes where both visit the shop on the same day $=5$

Number of outcomes where both visit the shop on different days $=25-5=20$

Total number of favourable outcomes $=20$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that both will visit the shop on different days $=\frac{20}{25}$

$=\frac{4}{5}$

The probability that both will visit the shop on different days is $\frac{4}{5}$.

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