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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 5 or a multiple of 2 ?
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 $5$ or a multiple of $2$ ? $\newline$ 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

5

or a multiple of

2

?

\newline

Answer:

Identify Multiples: First, we need to identify the multiples of $5$ and $2$ within the range of numbers $1$ through $14$ . Multiples of $5$ in this range are: $5$ and $10$ . Multiples of $2$ in this range are: $2$ , $4$ , $2$ $0$ , $2$ $1$ , $10$ , $2$ $3$ , and $14$ . Note that $10$ is a common multiple of both $5$ and $2$ , so it should only be counted once.
Count Favorable Outcomes: Next, we count the number of favorable outcomes, which are the numbers that are multiples of $5$ or $2$ . There are $2$ multiples of $5$ and $7$ multiples of $2$ , but since $10$ is a multiple of both, we have a total of $2 + 7 - 1 = 8$ favorable outcomes.
Calculate Probability: Now, we calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. $\newline$ The total number of possible outcomes is $14$ , as there are $14$ numbered areas on the spinner. $\newline$ Probability = Number of favorable outcomes / Total number of possible outcomes $\newline$ Probability = $\frac{8}{14}$
Simplify Fraction: Finally, we simplify the fraction $\frac{8}{14}$ to its lowest terms. $\newline$ $\frac{8}{14}$ can be simplified by dividing both the numerator and the denominator by $2$ . $\newline$ $8 \div 2 = 4$ $\newline$ $14 \div 2 = 7$ $\newline$ So, the simplified probability is $\frac{4}{7}$ .

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