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:
[tex]Prob.=\frac{1}{4}[/tex]
The proportion to find prediction is:
[tex]\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}[/tex]
The number of spins Addyson predicts is:
[tex]\begin{gathered} 1:4=12:x \\ \frac{1}{4}=\frac{12}{x} \\ Cross\text{ }multiply \\ x=12\times4 \\ x=48 \end{gathered}[/tex]
Hence, Addyson's prediction for the number of total spins before the letter D appears 12 times is:
[tex]x=48[/tex]
