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If a number is selected at random from the integers 1 through 12, what is the probability that it is not divisible by 3?


1. 1/6
2. 1/3
3. 2/3
4. 1/12

1 Answer

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Best answer
Correct Answer - Option 3 : 2/3

Concept:

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

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

Complement of an event:

The complement of an event is the subset of outcomes in the sample space that are not in the event.

The probability of the complement of an event is one minus the probability of the event.

P (A̅) = 1 - P (A) ⇒ P (A) = 1 - P (A̅)

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.

So, n(E) = 4

\(\rm P \left( {{\rm\text{Divisible by 3}}} \right) = \frac{{n\left( E \right)}}{{n\left( S \right)}} = \frac{4}{{12}} = \frac{1}{3}\)

Probability that it is not divisible by 3 = 1 - P(Divisible by 3) = 1 - 1/3 = 2/3

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