You roll a 6-sided die two times.:What is the probability of rolling a 6 and then rolling a 5?:Write your answer as a fraction or whole number.

Solution

\frac{1}{36}

Decimal

0.02777 \dots

Solution steps

Find the probability of rolling a 6:

\frac{1}{6}

Find the probability of then rolling a 5 ?::

\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}