Question

Eight points are spaced at intervals of one unit around a $2\times2$ square, as shown. Two of the $8$ points are chosen at random. What is the probability that the points are one unit apart?

$\ \dfrac{1}{4}$

$\ \dfrac{2}{7}$

$\ \dfrac{4}{11}$

$\ \dfrac{1}{2}$

$\ \dfrac{4}{7}$

Answer: B

Concepts:basic probability counting pairs

Difficulty rating: 1310

Solution:

Each dot has $2$ dots that are one unit away from it.

Therefore, regardless of the choice of the first dot, $2$ of the other $7$ dots would be within one unit, so the probability is $\dfrac 27.$

Thus, the answer is B .

2008 AMC 8 Problem 19

Answer: B

Difficulty rating: 1310

Solution:

Problem 19 in Other Years