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?

Question and options

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

B

is also a function?

Correct answer: A - $\frac{1}{8}$

A x B has 6 elements, so 2^6=64 relations; functions A->B number 2^3=8. Probability 8/64=1/8.