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single die is rolled twice. Find the probability of rolling an odd number the first time and a number greater than 2 the second time.

Solution

single die is rolled twice. Find the probability of rolling an odd number the first time and a number greater than 2 the second time.

Solution

\frac{1}{3}

Solution steps

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

\frac{1}{2}

Find the probability of a number greater than 2 the second time:

\frac{2}{3}

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{2}{3}

Cross-cancel common factor:

2

= \frac{1}{3}

Popular Examples

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