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If you spin the spinner $11$ times, what is the best prediction possible for the number of times it will not land on blue? $\newline$ Choices: $\newline$ (A) $9$ $\newline$ (B) $10$ $\newline$ (C) $11$ $\newline$ (D) $5$

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Full solution

Q. If you spin the spinner

11

times, what is the best prediction possible for the number of times it will not land on blue?

\newline

Choices:

\newline

(A)

9

\newline

(B)

10

\newline

(C)

11

\newline

(D)

5

Calculate Probability: First, we need to know the probability of the spinner not landing on blue. Assume the spinner has $4$ equal sections, and only $1$ section is blue. The probability of not landing on blue is $3$ out of $4$ sections, or $\frac{3}{4}$ .
Find Expected Number: Next, to find the expected number of times it will not land on blue in $11$ spins, multiply the probability by the number of spins: $(\frac{3}{4}) \times 11 = 8.25$ .
Round to Nearest Whole: Since we can't have a fraction of a spin, we round $8.25$ to the nearest whole number, which is $8$ . However, the choices given are $9$ , $10$ , $11$ , and $5$ . The closest and most reasonable choice from the options provided is $9$ .

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