Question

a spinner is split into six equal sections with the sections colored as labeled in the drawing. emily rolls a number cube labeled 1 - 6 and spins the spinner. what is the probability of emily rolling a 5 and spinning a yellow? a. $\frac{1}{36}$ b. $\frac{1}{18}$ c. $\frac{1}{3}$ d. $\frac{1}{2}$

Explanation:

Step1: Calculate probability of rolling a 5

A number - cube has 6 sides. The probability of rolling a 5 on a 6 - sided number cube is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 5) out of 6 possible outcomes.

Step2: Calculate probability of spinning a yellow

The spinner is split into 6 equal sections, and 2 of them are yellow. So the probability of spinning a yellow is $\frac{2}{6}=\frac{1}{3}$ since there are 2 favorable outcomes (spinning a yellow) out of 6 possible outcomes.

Step3: Use the multiplication rule for independent events

Since rolling the number - cube and spinning the spinner are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(\text{rolling a }5\text{ and spinning a yellow})=\frac{1}{6}\times\frac{1}{3}=\frac{1}{18}$.

Answer:

B. $\frac{1}{18}$