Let A = {1, 2, 3} and B = {a, b}. Assuming all relations from set A to set B are equally likely, what is the probability that a relation from A to B is also a function?

Set A has 3 elements and set B has 2 elements.

Number of relations from set A to B = $$2^{\left(3\times\ 2\right)}=2^6$$

(Number of relations from a set having $$m$$ elements to a set having $$n$$ elements is given by the formula $$2^{mn}$$)

Number of functions from set A to set B =$$2^3$$

(Number of functions from a set having $$m$$ elements to a set having $$n$$ elements is given by the formula $$n^m$$)

So, probability that a relation is also a function = $$\dfrac{2^3}{2^6}=\dfrac{1}{2^3}=\dfrac{1}{8}$$