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There is a spinner with 10 equal areas, numbered 1 through 10 . If the spinner is spun one time, what is the probability that the result is a multiple of 2 and a multiple of 3 ?
Answer:

There is a spinner with $10$ equal areas, numbered $1$ through $10$ . If the spinner is spun one time, what is the probability that the result is a multiple of $2$ and a multiple of $3$ ? $\newline$ Answer:

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Probability of simple events

Full solution

Q. There is a spinner with

10

equal areas, numbered

1

through

10

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

2

and a multiple of

3

?

\newline

Answer:

Identify Common Multiples: First, we need to identify the numbers on the spinner that are multiples of both $2$ and $3$ . Multiples of $2$ are $2$ , $4$ , $6$ , $8$ , and $10$ . Multiples of $3$ are $3$ , $6$ , and $3$ $1$ . The common multiples of both $2$ and $3$ are the numbers that are multiples of $6$ , since $6$ is the least common multiple of $2$ and $3$ .
List Multiples of $6$ : Now, we list the numbers on the spinner that are multiples of $6$ . These are $6$ itself and any other number that is a multiple of $6$ up to $10$ . Since the spinner only goes up to $10$ , the only multiple of $6$ is $6$ .
Calculate Probability: To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes. The favorable outcome is landing on $6$ , and there is only $1$ such outcome. The total number of possible outcomes is $10$ , as there are $10$ numbers on the spinner.
Final Probability: The probability is therefore $1$ favorable outcome divided by $10$ possible outcomes, which is $\frac{1}{10}$ or $0.1$ .

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