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There is a spinner with 12 equal areas, numbered 1 through 12 . If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 4 ?
Answer:

There is a spinner with $12$ equal areas, numbered $1$ through $12$ . If the spinner is spun one time, what is the probability that the result is a multiple of $3$ or a multiple of $4$ ? $\newline$ Answer:

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Probability of simple events

Full solution

Q. There is a spinner with

12

equal areas, numbered

1

through

12

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

3

or a multiple of

4

?

\newline

Answer:

Identify Multiples: First, we need to identify the multiples of $3$ and $4$ among the numbers $1$ through $12$ . $\newline$ Multiples of $3$ : $3$ , $6$ , $9$ , $12$ $\newline$ Multiples of $4$ : $4$ , $4$ $1$ , $12$
Combine Multiples: Next, we combine the multiples of $3$ and $4$ , making sure not to count any number twice. $\newline$ Combined multiples: $3$ , $4$ , $6$ , $8$ , $9$ , $12$
Count Favorable Outcomes: Now, we count the number of favorable outcomes, which are the combined multiples of $3$ and $4$ . $\newline$ Number of favorable outcomes: $6$ (since there are $6$ numbers that are multiples of $3$ or $4$ )
Count Total Outcomes: We then count the total number of possible outcomes when the spinner is spun. $\newline$ Total number of possible outcomes: $12$ (since there are $12$ numbers on the spinner)
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 = $\frac{6}{12}$
Simplify Fraction: Finally, we simplify the fraction to get the probability in its simplest form. Probability = $\frac{1}{2}$

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