Ex.15.2 Q1 Probability Solution - NCERT Maths Class 10

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Question

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?

Text Solution

 

What is known?

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 unknown?

The probability that both will visit the shop on

(i) the same day?

(ii) consecutive days?

(iii) different days

Reasoning:

To solve this question, first find out the total number of outcomes and all the possible outcomes. Now, to find the probability use the formula given below

\[\begin{align} \text{ Probability }=\frac{\text{ No of possible outcomes }}{\text{ Total no of outcomes}} \\\end{align}\]

Steps:

Total outcomes \(=\text{ }5\text{ }\times \text{ }5=25\)

(i) No of possible outcomes that both will visit the shop on the same day

\[\begin{align}&= \left( \text{T,T} \right)\text{,}\left( \text{W,W} \right)\text{,}\left( \text{TH,TH} \right)\text{,}\left( \text{F,F} \right)\text{,}\left( \text{S,S} \right)\\&=5\end{align}\]

Probability that both will visit the shop on the same day 
\[\begin{align}&=\frac{\text{No of possible outcomes }}{\text{ Total no of outcomes}} \\ & =\frac{5}{25} \\\end{align}\] 

(ii) No of possible outcomes that both will visit the shop on consecutive days

\[\begin{align}&= \left( \text{t,w} \right)\text{,}\left( \text{w,th} \right)\text{,}\left( \text{th,f} \right)\text{,}\left( \text{f,s} \right)\text{,}\left( \text{w,t} \right)\text{,}\left( \text{th,w} \right)\text{,}\left( \text{f,th} \right)\text{,}\left( \text{s,f} \right) \\&= 8\end{align}\]
Probability that both will visit the shop on the consecutive days
\[\begin{align}&=\frac{\text{No of possible outcomes}}{\text{Total no of outcomes}} \\ &=\frac{8}{25} \\\end{align}\]

(iii) No of possible outcomes that both will visit the shop on different days

\[\begin{align}&= \left( \text{t,w} \right)\text{,}\left( \text{w,th} \right)\text{,}\left( \text{th,f} \right)\text{,}\left( \text{f,s} \right)\text{,}\left( \text{w,t} \right)\text{,}\left( \text{th,w} \right)\text{,}\left( \text{f,th} \right)\text{,}\left( \text{s,f} \right) \\&= 8\end{align}\]

Probability that both will visit the shop on the different days
\[\begin{align}&=1-\frac{5}{25} \\&=\frac{20}{25} \\&=\frac{4}{5}\\\end{align}\]

  
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