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Question
Three faces of an ordinary dice are yellow, two faces are red and one face is blue. The dice is rolled 3 times. The probability that yellow red and blue face appear in the first second and third throws respectively, is
Options
- \[\frac{1}{36}\]
\[\frac{1}{6}\]
\[\frac{1}{30}\]
none of these
Solution
\[ \frac{1}{36}\]
\[P\left( \text{ yellow face } \right) = \frac{3}{6} = \frac{1}{2}\]
\[P\left( \text{ red face } \right) = \frac{2}{6} = \frac{1}{3}\]
\[P\left( \text{ one face } \right) = \frac{1}{6}\]
\[P\left( \text{ yellow face, red face and blue face appear in the required order }\right) = \frac{1}{2} \times \frac{1}{3} \times \frac{1}{6} = \frac{1}{36}\]
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