You roll a 6-sided die two times.What is the probability of rolling a 1 and then rolling a 2?

解

Y o u ro ll a 6 - s i d e d d i e tw o t im es . Wha t i s t h e p ro babi l i t y o f ro ll in g a 1 an d t h e n ro ll in g a 2 ?

\frac{1}{36}

十進法表記

0.02777 \dots

解答ステップ

Find the probability of rolling a 1:

\frac{1}{6}

Find the probability of then rolling a 2:

\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}