Question

The theoretical probability of spinning an even number on a spinner is 2/3 . The spinner has 8 even-numbered sections. How many sections are on the spinner?

Answer 1

Answer:  There are 12 sections on the spinner.

Step-by-step explanation:  Given that the  theoretical probability of spinning an even number on a spinner is $\dfrac{2}{3}.$ And the spinner has 8 even-numbered sections.

We are to find the number of sections on the spinner.

Let, x be the total number of sections on the spinner.

Then, the probability of spinning an even number on the spinner is given by

$\dfrac{8}{x}.$

According to the given information, we must have

$\dfrac{8}{x}=\dfrac{2}{3}\\\\\\\Rightarrow x=\dfrac{8\times 3}{2}\\\\\Rightarrow x=4\times 3\\\\\Rightarrow x=12.$

Thus, there are 12 sections on the spinner.

Answer 2

The probability helps us to know the chances of an event occurring. The number of sections that are on the spinner is 12.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

Let the total number of sections be x.

As it is given that the theoretical probability of spinning an even number on a spinner is 2/3, while the spinner has 8 even-numbered sections. Therefore, we can write the probability as,

${\rm Probability} = \dfrac{\text{Number of Even sections}}{\text{Total number of sections on the spinner}}\\\\\\\dfrac{2}{3} = \dfrac8x\\\\\\x = \dfrac{8 \times 3}{2}\\\\x=12$

Hence, the number of sections that are on the spinner is 12.

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