there is a spinner with 15 equal areas, numbered 1 through 15. if the spinner is spun one time, what is the…

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 2?

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 2?

Answer

Answer:

$\frac{8}{15}$

Explanation:

Step1: Find multiples of 5

Multiples of 5 from 1 - 15 are 5, 10, 15. So there are 3.

Step2: Find multiples of 2

Multiples of 2 from 1 - 15 are 2, 4, 6, 8, 10, 12, 14. So there are 7.

Step3: Find common multiples

Common multiple of 2 and 5 is 10. There is 1 common multiple.

Step4: Use inclusion - exclusion

Number of elements that are multiple of 5 or 2 is $3 + 7-1=9$.

Step5: Calculate probability

Probability = $\frac{9}{15}=\frac{3}{5}$ (There was a mistake above, correct way: Multiples of 5: 5, 10, 15; Multiples of 2: 2, 4, 6, 8, 10, 12, 14. After removing double - counted 10, the distinct numbers are 2, 4, 5, 6, 8, 10, 12, 14. There are 8. Probability = $\frac{8}{15}$)