Tom and Jerry pick randomly pick out a pair of parking spaces.

There are $\binom{n}2$ equiprobable pairs of parking spaces.

$n-1$ of the pairs consist of spaces that are not separated by any empty space.

$n-2$ of the pairs consist of spaces that are separated by exactly one empty space.

So: $$(n-1)+(n-2)=2n-3$$ of the pairs consist of spaces that are separated by at most one empty space.

Then the probability that Tom and Jerry pick out a pair consisting of spaces that are separated by at most one empty space equals:$$\frac{2n-3}{\binom{n}2}=\frac{4n-6}{n(n-1)}$$This based on the rule that probability equals number of favourable outcomes divided by number of possible outcomes. This rule works if the outcomes are equiprobable.

Tom and Jerry together randomly pick out a pair of parking spaces.

There are $\binom{n}2$ equiprobable pairs of parking spaces.

$n-1$ of the pairs consist of spaces that are not separated by any empty space.

$n-2$ of the pairs consist of spaces that are separated by exactly one empty space.

So: $$(n-1)+(n-2)=2n-3$$ of the pairs consist of spaces that are separated by at most one empty space.

Then the probability that Tom and Jerry pick out a pair consisting of spaces that are separated by at most one empty space equals:$$\frac{2n-3}{\binom{n}2}=\frac{4n-6}{n(n-1)}$$This based on the rule that probability equals number of favourable outcomes divided by number of possible outcomes. This rule works if the outcomes are equiprobable.

Tom and Jerry pick randomly pick out a pair of parking spaces.

There are $\binom{n}2$ equiprobable pairs of parking spaces.

$n-1$ of the pairs consist of spaces that are not separated by any empty space.

$n-2$ of the pairs consist of spaces that are separated by exactly one empty space.

So: $$(n-1)+(n-2)=2n-3$$ of the pairs consist of spaces that are separated by at most one empty space.

Then the probability that Tom and Jerry pick out a pair consisting of spaces that are separated by at most one empty space equals:$$\frac{2n-3}{\binom{n}2}=\frac{4n-6}{n(n-1)}$$

Tom and Jerry pick randomly pick out a pair of parking spaces.

There are $\binom{n}2$ equiprobable pairs of parking spaces.

$n-1$ of the pairs consist of spaces that are not separated by any empty space.

$n-2$ of the pairs consist of spaces that are separated by exactly one empty space.

So: $$(n-1)+(n-2)=2n-3$$ of the pairs consist of spaces that are separated by at most one empty space.

Then the probability that Tom and Jerry pick out a pair consisting of spaces that are separated by at most one empty space equals:$$\frac{2n-3}{\binom{n}2}=\frac{4n-6}{n(n-1)}$$This based on the rule that probability equals number of favourable outcomes divided by number of possible outcomes. This rule works if the outcomes are equiprobable.