Question

If a number is selected at random from the integers 1 through 12, what is the probability that it is even and divisible by 3?

1. 1/6
2. 1/3
3. 0
4. 1

Answer 1

Correct Answer - Option 1 : 1/6

Concept:

If S is a sample space and E is a favourable event then the probability of E is given by:

\(\rm P(E)=\frac{n(E)}{n(S)}\)

Calculation:

The set, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} is a sample space for the given experiment.

So, n(S) = 12

The set, E = {3, 6, 9, 12} contains the numbers that are divisible by 3.

Let set F = Number is even and divisible by 3

So, The set F = {6,12}

n(F) = 12

\(\rm P \left( {{\rm \text{Even and divisible by 3}}} \right) = \frac{{n\left( F \right)}}{{n\left( S \right)}} = \frac{2}{{12}} = \frac{1}{6}\)