Probability

A number from 1 to 20 is selected at random. What is the probability the selected number is even and a multiple of three?

List the elements in both of the event spaces and find the intersection.

The even numbers are

{2, 4, 6, 8, 10, 12, 14, 16, 18, 20 }

From this set, the multiples of three are

{6, 12, 18 }

Calculate the probability of both events.

\( P(\text{Multiple of three and Even}) \) \[ \begin{align} &= \frac{\text{Elements in Intersection}}{\text{Elements in sample space}} \quad \\ &= \frac{3}{20} \quad \\ \end{align} \ \]

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Look through the options below and select the one you think is the best response. You will gain most benefit if you work the problem with pen and paper as you go, i.e. decide what you think is the correct option and write down what you think the result will be before you click. If the next step doesn't display, click another option.

What is a systematic way to find the elements in the required set?

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Now You Try:

A number from 1 to 30 is selected at random. What is the probability the selected number is odd and a multiple of five?