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 3 or a multiple of 4?

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 3 or a multiple of 4?

Answer

Explanation:

Step1: Find multiples of 3

Multiples of 3 from 1 - 15: 3, 6, 9, 12, 15. So (n(3)=5)

Step2: Find multiples of 4

Multiples of 4 from 1 - 15: 4, 8, 12. So (n(4)=3)

Step3: Find common multiples (LCM of 3 and 4 = 12)

Common multiple: 12. So (n(3\cap4) = 1)

Step4: Use formula (P(A\cup B)=P(A)+P(B)-P(A\cap B))

Total outcomes (n = 15) (P(3\cup4)=\frac{n(3)+n(4)-n(3\cap4)}{n}=\frac{5 + 3-1}{15}) (=\frac{7}{15})

Answer:

(\frac{7}{15})