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There is a spinner with 14 equal areas, numbered 1 through 14 . If the spinner is spun one time, what is the probability that the result is a multiple of 6 or a multiple of 4 ?
Answer:

There is a spinner with $14$ equal areas, numbered $1$ through $14$ . If the spinner is spun one time, what is the probability that the result is a multiple of $6$ or a multiple of $4$ ? $\newline$ Answer:

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Probability of simple events

Full solution

Q. There is a spinner with

14

equal areas, numbered

1

through

14

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

6

or a multiple of

4

?

\newline

Answer:

Identify Multiples: First, we need to identify the multiples of $6$ and the multiples of $4$ among the numbers $1$ through $14$ . $\newline$ Multiples of $6$ : $6$ , $12$ $\newline$ Multiples of $4$ : $4$ , $8$ , $12$
Combine Multiples: Next, we combine the multiples of $6$ and $4$ , making sure not to count any number twice. $\newline$ Combined multiples: $4$ , $6$ , $8$ , $12$
Count Favorable Outcomes: Now, we count the number of favorable outcomes, which are the combined multiples. $\newline$ Number of favorable outcomes: $4$ (since $4$ , $6$ , $8$ , and $12$ are the numbers that are multiples of $4$ or $6$ )
Count Total Outcomes: We then count the total number of possible outcomes, which is the total number of areas on the spinner. $\newline$ Total number of possible outcomes: $14$
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 = $\frac{4}{14}$
Simplify Fraction: Finally, we simplify the fraction to get the probability in its simplest form. Probability = $\frac{2}{7}$ (since $4$ and $14$ are both divisible by $2$ )

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