Question

Seven persons draw a lottery for occupancy of $6$ seats inside a first-class railway compartment. The probability that $2$ specified persons will obtain opposite seats,
A. $\dfrac{1}{7}$
B. $\dfrac{2}{7}$
C. $\dfrac{5}{7}$
D. None of these

Answer 1

We are given a group of seven people in which they draw a lottery for occupancy of six seats in a railway first-class compartment and we need to find the probability that two specified persons sit opposite to each other. For that, we need to find the probability of each person that they got one seat and then find the probability of sitting opposite to each other.

Complete step by step answer:
Let the two specified persons be A and B. Now the probability that person A gets a seat in the compartment of six seats out of seven people is,
$A = \dfrac{6}{7}$
Now the probability of person B that person B sits opposite to person A in the compartment of five seats since one is already occupied by person A out of six people left in the group is
$B = \dfrac{1}{6}$ since there is only one opposite sit to the person A. Therefore the probability that B is opposite to A is
$P = \dfrac{6}{7} \times \dfrac{1}{7} \\\ \therefore P= \dfrac{1}{7}$

Hence option A is the correct answer.

Additional information: Probability is a mathematical term for the likelihood that something will occur. It is the ability to understand and estimate the probability of a different combination of outcomes. The accomplishment of action without any prior decisions results in a set of possible outcomes. The action is called the random experiment. And the result of any random experiment is known as the outcome.

Note: The possibility of occurrence of each outcome is the same in a particular event then the event is said to have equally likely outcomes like in this case we had six seats and a person getting any seat is equally likely. We multiplied both the probabilities and not added them because the first event happening impacts the probability of the second event.