Question

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday) is equally likely to visit the shop on any day as on another day.what is the probability that both will visit the shop.
(1)the same day?
(2)consecutive day?
(3)different day?


Note:- •step by step explanation.
•Don't copy❌
•Proper answer shoud be needed.

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Answer 1

The total number of days from Tuesday to Saturday = 5

Hence, both of them can reach the shop in 5 ways.

So, total number of outcomes = 5 × 5 = 25 ways

They can reach on the same day in 5 ways, i.e.

(Tuesday, Tuesday) ; (Wednesday, Wednesday) ; (Thursday, Thursday) ; (Friday, Friday) ; (Saturday, Saturday) 

1) Probability of reaching the same day -

= 5/25 

= 1/5 
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They can reach on consecutive days in following 8 ways :

(Tuesday, Wednesday) ; (Wednesday, Tuesday) ; (Wednesday, Thursday) ; (Thursday, Wednesday) ; (Thursday, Friday) ; (Friday, Thursday) ; (Friday, Saturday) ; (Saturday, Friday)

2) Probability of reaching on consecutive days -

= 8/25

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3) Probability of reaching on different days -

As, Probability of reaching on same days = 1/5

Hence, probability of reaching on different days = 1 - 1/5 

= 4/5

Answer.

Answer 2

Given : Shyam and Ekta visit shop in the same week(Tuesday to Saturday).

There are total of 5 days.

Shyam can go to the shop in 5 days and Ekta can go to the shop in 5 days.

So, the possible outcomes are n(S) : 5 * 5 = 25.

(i) The same day:

Let E₁ be the event that they both will visit the shop on same day.

E₁ = (T,T),(W,W),(Thu,Thu,),(Fri,Fri),(Sat,Sat)

   = 5.

Required probability P(E₁) = n(E₁)/n(S)

                                          = 5/25

                                          = 1/5.

(ii) Consecutive days:

Let E₂ be the event that they both the shop on consecutive days.

E₂ = (Tue,Wed), (Wed,Tue),(Wed,Thu),(Thu,Wed), (Thu,Fri),(Fri,Thu),(Fri,Sat),(Sat,Fri)

   = 8.

Required probability P(E₂) = n(E₂)/n(S)

                                           = 8/25.

(iii) Different days:

Required probability P(E) = 1 - P(on same day)

                                         = 1 - 1/5

                                         = 4/5

Hope it helps!

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