Question

Please reference the attached image for the problem that I need solved & explained. Thank you

Answer 1

Explanation

We are given the following:

• A spinner has 4 equally sized sections labeled A to D.

We are required to determine Addyson's prediction for the number of total spins before the letter D appears 12 times.

Since we know that each section is equal to one another, then their probability is also equal.

The probability of getting a D in 1 spin becomes:

`Prob.=(1)/(4)`

The proportion to find prediction is:

`\begin{gathered} Proportion\to1:4 \\ For\text{ }every\text{ }4\text{ }spins,D\text{ }is\text{ }expected\text{ }to\text{ }appear\text{ }once \end{gathered}`

The number of spins Addyson predicts is:

`\begin{gathered} 1:4=12:x \\ (1)/(4)=(12)/(x) \\ Cross\text{ }multiply \\ x=12*4 \\ x=48 \end{gathered}`

Hence, Addyson's prediction for the number of total spins before the letter D appears 12 times is:

`x=48`