# A number cube is rolled and a coin is tossed. What is the probability of rolling a 5 and tossing tails?

Feb 10, 2016

Because these events are independent, you can get the probability of of rolling a 5 and tossing tails by multiplying the probabilities of the two events together.

This gives you $P = \left(\frac{1}{6}\right) \cdot \left(\frac{1}{2}\right) = \frac{1}{12}$

#### Explanation:

Assuming the cube is 6-sided and is fair, the probability of rolling a $5$ is $\frac{1}{6}$ (because there is an equal chance of rolling a $1$, $2$, $3$, $4$, $5$, and $6$, so the probability of each is 1 divided by the total number of options).

Assuming the coin is fair, the probability of tossing tails is $\frac{1}{2}$ (because there are two, equally likely options).

Therefore, to get the probability of rolling a $5$ AND tossing tails, you multiply $\left(\frac{1}{6}\right)$ by $\left(\frac{1}{2}\right)$, and get the answer $\left(\frac{1}{12}\right)$.

Note: This is only possible because the events are independent. If the outcome of one affected the outcome of the other, you would not be able to simply multiply the probabilities together