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 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 3 or a multiple of 2?

Answer

Explanation:

Step1: Find multiples of 2 and 3

Multiples of 2 from 1 - 15: 2, 4, 6, 8, 10, 12, 14 (7 numbers). Multiples of 3 from 1 - 15: 3, 6, 9, 12, 15 (5 numbers).

Step2: Find common multiples

Common multiples of 2 and 3 (i.e., multiples of 6) from 1 - 15 are 6 and 12 (2 numbers).

Step3: Use the inclusion - exclusion principle

The number of elements that are either a multiple of 2 or a multiple of 3 is (7 + 5-2=10).

Step4: Calculate the probability

The probability (P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}). Total number of outcomes is 15. So (P = \frac{10}{15}=\frac{2}{3}).

Answer:

(\frac{2}{3})