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Popular Word Problems >

You roll a 6-sided die two times. what is the probability of rolling a 5 and then rolling a 4?

Solution

Y o u ro ll a 6 - s i d e d d i e tw o t im es . w ha t i s t h e p ro babi l i t y o f ro ll in g a 5 an d t h e n ro ll in g a 4 ?

Solution

\frac{1}{36}

+1

Decimal

0.02777 \dots

Solution steps

Find the probability of rolling a 5:

\frac{1}{6}

Find the probability of then rolling a 4:

\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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