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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 4 or a multiple of 3 ?
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 $4$ or a multiple of $3$ ? $\newline$ 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

4

or a multiple of

3

?

\newline

Answer:

Identify Multiples: Identify the multiples of $4$ and $3$ within the range of numbers on the spinner ( $1$ through $14$ ). $\newline$ Multiples of $4$ : $4$ , $8$ , $12$ $\newline$ Multiples of $3$ : $3$ , $3$ $0$ , $3$ $1$ , $12$
Combine Lists: Combine the lists of multiples, making sure to count the common multiple ( $12$ in this case) only once. $\newline$ Combined list of unique multiples: $3, 4, 6, 8, 9, 12$
Count Unique Multiples: Count the number of unique multiples from the combined list. $\newline$ Number of unique multiples: $6$
Calculate Probability: Calculate the probability by dividing the number of unique multiples by the total number of areas on the spinner. $\newline$ Probability = $\frac{\text{Number of unique multiples}}{\text{Total areas on the spinner}}$ $\newline$ Probability = $\frac{6}{14}$
Simplify Fraction: Simplify the fraction to get the final probability. $\newline$ Probability = $\frac{3}{7}$

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