Question

if you spin the spinner 80 times, what is the best possible prediction for the number of times it will land on an 8?
spinner image showing numbers 2,3,4,5,6,7,8,9 in 8 equal sections
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Explanation:

Step1: Determine the number of equal sections on the spinner.

Looking at the spinner, we can see that it is divided into 8 equal - sized sections (the numbers 2, 3, 4, 5, 6, 7, 8, 9 are each in their own section). So the total number of possible outcomes, \(n = 8\).

Step2: Find the probability of landing on 8.

The probability of an event \(A\) (in this case, landing on 8) is given by the formula \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\). The number of favorable outcomes (landing on 8) is 1, and the total number of possible outcomes is 8. So \(P(\text{landing on }8)=\frac{1}{8}\).

Step3: Calculate the expected number of times landing on 8 in 80 spins.

The expected number of times an event occurs in \(N\) trials is given by \(E = N\times P(A)\). Here, \(N = 80\) (the number of spins) and \(P(A)=\frac{1}{8}\). So we calculate \(E=80\times\frac{1}{8}\).
\(80\times\frac{1}{8}=\frac{80}{8} = 10\).

Answer:

10