Find the probability of choosing an item from the intersection of following sets

Question

Find the probability of choosing an item from the intersection of following sets

    Set A : {1, 5, 10, 14, 22}

   Set B : {5, 14, 20, 22, 27}

Answer 1

The intersection is what's in common.

A ∩ B = {5,22}

What's the probability of choosing one of these?

Answer 2

I will assume that the space S contains exactly A U B.

S = A U B = { 1, 5, 10, 14, 20, 22, 27}

Function n(S) denotes the number of elements in S. In our case,

n(S) = 7.

Similarly,

A ∩ B = {5, 14, 22}

n(A ∩ B) = 3.

Using the above notation, we find probability a number to be in the intersection A ∩ B:

P(A ∩ B) = n(A ∩ B)/n(S)

P(A ∩ B) = 3/7.