Question

it's a probability question please answer this.....

Answer 1

Shom and Ekta are visiting the shop between Tuesday and Saturday.
So they can visit on {Tuesday, Wednesday, Thursday, Friday or Saturday}
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Find the sample space:

They can visit the shop on any day of the given 5 days.

Since there are two persons, Total possible outcomes of them visiting the shop on those days = 5^2 = 25.

(It's like when you roll one dice, total outcomes is 6 and when you roll two dice, total outcomes = 6^2 = 36. If you are unclear, ask in comment)
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i) Probability of visiting the same day

Find the total number of outcomes when they visit on the same day.

if Shom visits on Tuesday, then Ekta visits on Tuesday. Similarly for Wednesday, Thursday, Friday and Saturday.

So total favourable outcomes = 5

Probability of visiting the same day = 5/25 = 1/5
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ii) Probability of visiting the consecutive days

Find the total number of outcomes when they visit on consecutive days

1. If Shom visits on Tuesday, then Ekta visits on Wednesday

2. If Shom visits on Wednesday, then Ekta visits on Thursday

3. If Shom visits on thursday, then Ekta visits on Friday

4. If Shom visits on Friday, then Ekta visits on Saturday

Total 4 outcomes here.

Similarly, if Ekta visits on Tuesday, then Shom visits on Wednesday

and 3 more cases. total 4 here.

overall total = 4+4 = 8

So Probability of visiting the consecutive days = 8/25
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iii) Probability of visiting the different days

Since there are 5 outcomes where they visit on same day,

number of outcomes where they visit on different days = 25 - 5 = 20

Probability of visiting the different days = 20/25 = 4/5