Answer

Verified

478.2k+ 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,

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

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

10 examples of friction in our daily life

One cusec is equal to how many liters class 8 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What is the type of food and mode of feeding of the class 11 biology CBSE

Trending doubts

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What organs are located on the left side of your body class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

Draw a diagram of a plant cell and label at least eight class 11 biology CBSE

Can anyone list 10 advantages and disadvantages of friction

What are the disadvantages of O negative blood class 11 biology CBSE

Difference between physical and chemical change class 11 chemistry CBSE