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A fair die is to be thrown twice. What is the probability that the result on the first thrown is 5 and an even number on the second throw?

الحلّ

A fair die is to be thrown twice. What is the probability that the result on the first thrown is 5 and an even number on the second throw?

الحلّ

\frac{1}{12}

خطوات الحلّ

Find the probability of the result on the first thrown is 5:

\frac{1}{6}

Find the probability of an even number on the second throw:

\frac{1}{2}

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}{2}

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

= \frac{1}{12}

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