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Popular Word Problems >

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 s in g l e d i e i s ro ll e d tw i ce . F in d t h e p ro babi l i t y o f ro ll in g an o dd n u mb er t h e f i rs t t im e an d a n u mb er g re a t er t han 1 t h e seco n d t im e .

Solution

\frac{5}{12}

+1

Decimal

0.41666 \dots

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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