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There is a spinner with 13 equal areas, numbered 1 through 13 . If the spinner is spun one time, what is the probability that the result is a multiple of 4 or a multiple of 6 ?
Answer:

There is a spinner with $13$ equal areas, numbered $1$ through $13$ . If the spinner is spun one time, what is the probability that the result is a multiple of $4$ or a multiple of $6$ ? $\newline$ Answer:

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Probability of simple events

Full solution

Q. There is a spinner with

13

equal areas, numbered

1

through

13

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

4

or a multiple of

6

?

\newline

Answer:

Identify Multiples: First, we need to identify the multiples of $4$ and $6$ within the range of numbers $1$ through $13$ . $\newline$ Multiples of $4$ : $4$ , $8$ , $12$ $\newline$ Multiples of $6$ : $6$ , $12$
Combine Multiples: Next, we combine the multiples of $4$ and $6$ , making sure not to count any number more than once since $12$ is a common multiple. $\newline$ Combined multiples: $4$ , $8$ , $12$ , $6$
Count Favorable Outcomes: Now, we count the number of favorable outcomes, which are the combined multiples of $4$ and $6$ . $\newline$ Number of favorable outcomes: $4$ (since there are four numbers that are either a multiple of $4$ or $6$ )
Determine Total Outcomes: We then determine the total number of possible outcomes, which is the number of areas on the spinner. $\newline$ Total number of possible outcomes: $13$
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 = $\frac{4}{13}$

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