there is a spinner with 13 equal areas, numbered 1 through 13. if the spinner is spun one time, what is the…

there is a spinner with 13 equal areas, numbered 1 through 13. if the spinner is spun one time, what is the probability that the result is a multiple of 3 and a multiple of 4?

there is a spinner with 13 equal areas, numbered 1 through 13. if the spinner is spun one time, what is the probability that the result is a multiple of 3 and a multiple of 4?

Answer

Explanation:

Step1: Find the numbers that are multiples of 3 and 4

The least - common multiple of 3 and 4 is (LCM(3,4)=12). The numbers from 1 to 13 that are multiples of both 3 and 4 are the numbers that are multiples of (LCM(3,4)). In the range (1\leq n\leq13), when (n = 12) (since (12\div3 = 4) and (12\div4=3)), there is 1 such number.

Step2: Calculate the probability

The probability formula is (P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}). The total number of outcomes when spinning the spinner is (n = 13) (since there are 13 equal - sized areas numbered 1 through 13). The number of favorable outcomes (a number that is a multiple of 3 and 4) is (m = 1). So, (P=\frac{1}{13}).

Answer:

(\frac{1}{13})