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There is a spinner with 11 equal areas, numbered 1 through 11 . If the spinner is spun one time, what is the probability that the result is a multiple of 2 or a multiple of 3 ?
Answer:

There is a spinner with $11$ equal areas, numbered $1$ through $11$ . If the spinner is spun one time, what is the probability that the result is a multiple of $2$ or a multiple of $3$ ? $\newline$ Answer:

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Probability of simple events

Full solution

Q. There is a spinner with

11

equal areas, numbered

1

through

11

. If the spinner is spun one time, what is the probability that the result is a multiple of

2

or a multiple of

3

?

\newline

Answer:

Identify Multiples: First, we need to identify the numbers from $1$ to $11$ that are multiples of $2$ or multiples of $3$ . Multiples of $2$ between $1$ and $11$ are: $2$ , $4$ , $6$ , $11$ $0$ , $11$ $1$ . Multiples of $3$ between $1$ and $11$ are: $3$ , $6$ , $11$ $7$ .
Combine Sets: Next, we combine the two sets of multiples, making sure not to count any number twice. $\newline$ The combined set of multiples of $2$ or $3$ is: $2$ , $3$ , $4$ , $6$ , $8$ , $9$ , $10$ .
Count Favorable Outcomes: Now, we count the number of favorable outcomes, which are the numbers in our combined set. $\newline$ There are $7$ favorable outcomes.
Count Total Outcomes: We then count the total number of possible outcomes, which is the total number of areas on the spinner. $\newline$ There are $11$ possible outcomes.
Calculate Probability: To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes. $\newline$ Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ $\newline$ Probability = $\frac{7}{11}$

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