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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 5 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 $5$ 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

5

or a multiple of

3

?

\newline

Answer:

Identify Multiples: First, we need to identify the multiples of $5$ and $3$ among the numbers $1$ through $15$ . $\newline$ Multiples of $5$ in this range are: $5$ , $10$ , and $15$ . $\newline$ Multiples of $3$ in this range are: $3$ , $3$ $0$ , $3$ $1$ , $3$ $2$ , and $15$ . $\newline$ Note that $15$ is a common multiple of both $5$ and $3$ , so it should only be counted once.
Count Favorable Outcomes: Next, we count the number of favorable outcomes. There are $3$ multiples of $5$ and $5$ multiples of $3$ , but since $15$ is a multiple of both, we subtract one to avoid double-counting. $\newline$ So, the total number of favorable outcomes is $3$ (multiples of $5$ ) + $4$ (multiples of $3$ , excluding the double-counted $15$ ) = $5$ $0$ .
Calculate Probability: Now, we calculate the probability. The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. $\newline$ The total number of possible outcomes is $15$ , as there are $15$ numbered areas on the spinner. $\newline$ The probability is therefore $7$ (favorable outcomes) $\div$ $15$ (total outcomes).
Simplify Fraction: Finally, we simplify the fraction $\frac{7}{15}$ if possible. However, $7$ and $15$ have no common factors other than $1$ , so the fraction is already in its simplest form. $\newline$ The probability of spinning a multiple of $5$ or $3$ is $\frac{7}{15}$ .

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