Question

a spinner and a fair number cube are used in a game. the spinner has an equal chance of landing on 1 of 4 colors: red, purple, blue, or green. the faces of the cube are labeled 1 through 6. what is the probability of a player spinning the color red and then rolling a 5 or 6? a $\frac{3}{10}$ b $\frac{1}{8}$ c $\frac{1}{12}$ d $\frac{1}{24}$

Explanation:

Step1: Find probability of spinning red

The spinner has 4 equal - chance colors (red, purple, blue, green). So the probability of spinning red, $P(\text{red})=\frac{\text{Number of red sections}}{\text{Total number of sections}}=\frac{1}{4}$.

Step2: Find probability of rolling 5 or 6

A fair number cube has 6 faces labeled 1 - 6. The number of favorable outcomes (rolling 5 or 6) is 2. So the probability of rolling 5 or 6, $P(5\text{ or }6)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{2}{6}=\frac{1}{3}$.

Step3: Find the combined probability

Since spinning the spinner and rolling the cube are independent events, the probability of both events happening is the product of their individual probabilities. So $P(\text{red and (5 or 6)}) = P(\text{red})\times P(5\text{ or }6)=\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$.

Answer:

C. $\frac{1}{12}$