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Probability — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsProbability4 Marks
Question
Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on:
  1. The same day?
  2. Different days?
  3. Consecutive days?
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Answer

Given: Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another.
To Find: Probability that both will visit the shop on:
  • The same day.
  • Different days.
  • Consecutive days
Two customers can visit the shop on two days in $6 \times 6 = 36$ ways.
Hence total number of ways $= 36$
  1. Two customer can visit the shop on any day of the week i.e.
$MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY$
Favorable number of ways $= 6$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of the customer visiting the shop on the same day $=\frac{6}{36}=\frac{1}{6}$
  1. We know that sum of probability of occurrence of an event and probability of non occurrence of an event is $1.$
$\text{P(E)}=\text{P}(\bar{\text{E}})=1$
$\frac{1}{6}+\text{P}(\bar{\text{E}})=1$
$\text{P}(\bar{\text{E}})=1-\frac{1}{6}$
Hence probability of the customer visiting the shop on the different day is $\frac{5}{6}$
  1. Two costumer can visit the shop in two consecutive days in the following ways:
$(MONDAY, TUESDAY), (WEDNESDAY, THURSDAY), (THURSDAY, FRIDAY) (FRIDAY, SATURDAY)$
Favorable number of ways $=5$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of the customer visiting the shop on two consecutive days $=\frac{5}{36}$

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