Question

Mary is playing a game in which she rolls one die and spins a spinner. What is the probability she will get both the 3 and black she needs to win the game?

Answer 1

Let m denote the total number of outcomes rolling a die, therefore the probability of getting "3" is:

$P(3 \ on \ die)=\frac{1}{m}$

Let n denote the total number of outcomes spinning a spinner, therefore the probability of getting "black" is:

$P(black)=\frac{1}{n}$

Thus the probability to get both the 3 and black:

$P(3\ and\ black)=\frac{1}{m}\cdot \frac{1}{n}=\frac{1}{mn}$

Answer: $\frac{1}{mn}$