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A single die is rolled twice. Find the probability of rolling an odd number the first time and a number greater than 1 the second time.

Solution

A single die is rolled twice. Find the probability of rolling an odd number the first time and a number greater than 1 the second time.

Solution

\frac{5}{12}

Solution steps

Find the probability of rolling an odd number the first time:

\frac{1}{2}

Find the probability of a number greater than 1 the second time:

\frac{5}{6}

Since the events are independent, Use the formula

P (X_{1} \land X_{2} \land \dots \land X_{k}) = P (X_{1}) \cdot P (X_{2}) \cdot \dots \cdot P (X_{k})

= \frac{1}{2} \cdot \frac{5}{6}

\frac{1}{2} \cdot \frac{5}{6} = \frac{5}{12}

= \frac{5}{12}

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