Discussion

Question:

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?

Explanation:

For two sets A and B with m and n elements respectively.
Total relations = 2^{m × n}
Total functions from A to B = n^m

Here, A = {1, 2, 3} i.e., 3 elements and B = {a, b} i.e., 2 elements.

∴ Total relations = 2^{3 × 2} = 64
Total functions from A to B = 2³ = 8

⇒ Required probability = 8/68 = 1/8.

Hence, option (a).

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