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Question
A die is thrown. Find the probability of getting:
a multiple of 2 or 3
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Solution
\[\text{ When a die is thrown, the possible outcomes are 1, 2, 3, 4, 5 and 6 }. \]
\[\text{ Thus, the sample space will be as follows }: \]
\[S = \left\{ 1, 2, 3, 4, 5, 6 \right\}\]
\[\text{ Let A be the event of getting multiples of 2 or 3 }. \]
\[\text{ Here, the multiples of 2 are 2, 4, 6 and the multiples of 3 are 3 and 6 } . \]
\[\text{ Therefore, the favourable outcomes are 2, 3, 4 and 6 } . \]
\[\text{ Hence, the probability of getting a multiple of 2 or 3 is as follows }: \]
\[P\left( A \right) = \frac{\text{ Number of favorable outcomes }}{\text{ Total number of outcomes }} = \frac{4}{6} = \frac{2}{3}\]
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