Let's say you are at a table with $5$ others, everyone is seated randomly around a $6$ person table, and you only know $1$ person at this party.
- What is the likelihood you sit next to the individual that you know?
- What is the likelihood you are seated opposite to the person that you know?
- What is the likelihood that you sit next to two strangers?
The table has $6$ seats so if you sit in any one seat then there are $5$ chairs left over. Since your friend can be seated on either side of you that leaves 3 chairs. With that reasoning would it be $1/3$ ($2/6$)?
Best Answer
The answer to #1 is not $\frac26$ but $\frac25$, since you can consider your own seat fixed without loss of generality, leaving 5 chairs, two of which are adjacent to you. Similarly, the answers for #2 and #3 are $\frac15$ and $\frac35$ respectively, both obtained by counting the number of chairs where the desired result is obtained by your friend sitting there by the number of empty chairs.