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פּוֹפּוּלָרִי Word Problems >

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.

פתרון

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 g e tt in g a 3 t h e f i rs t t im e an d 3 t h e seco n d t im e . E x p ress t h e p ro babi l i t y a s a s im pl i f i e d f r a c t i o n .

פתרון

\frac{1}{36}

+1

עשרוני

0.02777 \dots

צעדי פתרון

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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