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There is a spinner with 15 equal areas, numbered 1 through 15 . 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 $15$ equal areas, numbered $1$ through $15$ . 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

15

equal areas, numbered

1

through

15

. 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: First, we need to identify the multiples of $4$ and $3$ within the range of $1$ to $15$ . Multiples of $4$ are: $4$ , $8$ , $12$ . Multiples of $3$ are: $3$ , $3$ $0$ , $3$ $1$ , $12$ , $15$ .
Combine Sets: Next, we combine the two sets of multiples, making sure to count the common multiple ( $12$ in this case) only once. $\newline$ The combined set of multiples is: $3, 4, 6, 8, 9, 12, 15$ .
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.
Determine Total Outcomes: We then determine the total number of possible outcomes, which is the total number of areas on the spinner. $\newline$ There are $15$ 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 = $\frac{7}{15}$

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