Question

In a board game, each player must roll a number cube and spin a spinner. The number cube is labeled with the numbers 1 through 6 and the spinnerconsists of 8 equal parts shown below. What is the probability you will roll a 3 and land on red?1/103/81/242/3

Answer 1

In the question above, we can see that there are two experiments.

Experiment 1: Roll a number cube

Experiment 2: Spin a spinner

In experiment 1, rolling a number cube, we know that a cube has 6 sides, therefore there are 6 possible outcomes. These are (1,2,3,4,5,6). The set of possible outcomes is what we call sample space.

In experiment 2, spinning the spinner, it is mentioned that there 8 equal parts, and these equal parts have some of the parts labeled the same. Based on the spinner, we have 4 possible outcomes and these are (red, green, yellow, blue). To be exact, we have 2 reds, 4 blues, 1 green, and 1 yellow. A total of 8 parts in the spinner.

To answer the question, we have to get the probability of each event (roll a 3 and land on red) and then multiply it to each other. We multiply it because these are two independent combined events.

The probability of an event can be solved using the following formula:

`\begin{gathered} P(A)=\frac{no.\text{of times the event can occur}}{\text{total possible outcomes}} \\ \end{gathered}`

For the event rolling a 3, we have 1/6 because there is only one side that is 3 over the 6 sides.

For the event landing on red, we have 2/8 or 1/4 because there are 2 reds over the 8 parts of the spinner.

Therefore, the probability of rolling a 3 and landing on red will be 1/24 as shown below.

`(1)/(6)*(2)/(8)=(2)/(48)=(1)/(24)`