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single die is rolled twice. Find the probability of getting a 3 the first time and 3 the second time. Express the probability as a simplified fraction.

Solution

Solution

\frac{1}{36}

Solution steps

Find the probability of getting a 3 the first time:

\frac{1}{6}

Find the probability of 3 the second time.:

\frac{1}{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}{6} \cdot \frac{1}{6}

\frac{1}{6} \cdot \frac{1}{6} = \frac{1}{36}

= \frac{1}{36}

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