# Seven persons draw lots for the occupancy of the six seats in a first class railway compartments:

Find the chance

(1) that two specified persons obtain opposite seats,

(2) that they obtain adjacent seats on the same side.

Answer

Verified

328.5k+ views

Hint: Whenever a question is given of this sort where we are supposed to find the chances of an event happening, we use probability.

Let us consider 2 people X and Y.

The condition is the seats should be opposite to each other and there will be only one seat opposite to X.

Now, the probability that Y sits opposite to \[X = \dfrac{6}{7} \times \dfrac{1}{7} = \dfrac{1}{7}\]

So the answer for the first part \[ = \dfrac{1}{7}\]

2) Total there are 7 persons, we have to select 2 adjacent seats that can be done using combination.

Therefore,

The seats can be selected in ${}^7{C_2}ways = 21ways$

Note: ${}^7{C_2}$ is the total ways in which the seat can be taken by the two people, it is not the final answer. The final answer will be the probability of the favourable condition divided by the total outcomes.

Now, X and Y can be seated adjacent in 4 ways, which is our favourable condition.

Now, to find the probability we are going to use the formula of probability

Therefore,

\[Required{\text{ }}Probability = \dfrac{{Favourable\,Condition}}{{Total\,Conditions}} = \dfrac{4}{{21}}\]

Let us consider 2 people X and Y.

- 1) Now, the probability of X getting a seat \[ = \dfrac{6}{7}\]

The condition is the seats should be opposite to each other and there will be only one seat opposite to X.

Now, the probability that Y sits opposite to \[X = \dfrac{6}{7} \times \dfrac{1}{7} = \dfrac{1}{7}\]

So the answer for the first part \[ = \dfrac{1}{7}\]

Therefore,

The seats can be selected in ${}^7{C_2}ways = 21ways$

Note: ${}^7{C_2}$ is the total ways in which the seat can be taken by the two people, it is not the final answer. The final answer will be the probability of the favourable condition divided by the total outcomes.

Now, X and Y can be seated adjacent in 4 ways, which is our favourable condition.

Now, to find the probability we are going to use the formula of probability

Therefore,

\[Required{\text{ }}Probability = \dfrac{{Favourable\,Condition}}{{Total\,Conditions}} = \dfrac{4}{{21}}\]

Last updated date: 01st Jun 2023

â€¢

Total views: 328.5k

â€¢

Views today: 4.86k

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main