Question

There is a spinner with 12 equal areas, numbered 1 through 12. 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 1

if the result is multiple of 3 then the answer would be 1 by 4

and if the result is a multiple of 4 then the answer would be 1 by 3

Answer 2

Answer : The probability for a multiple of 3 or a multiple of 4 is, $\frac{1}{3}$ and $\frac{1}{4}$ respectively.

Step-by-step explanation :

Probability : It is defined as the extent to which an event is likely to occur. That means, it is measured by the ratio of the favorable outcomes to the total number of possible outcomes.

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of favorable outcomes}}$

Favorable outcomes are, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

First we have to calculate the probability that the result is a multiple of 3.

Favorable outcomes for a multiple of 3 are, 3, 6, 9, 12

Number of favorable outcomes for a multiple of 3 = 4

Total number of outcomes = 12

$\text{Probability}=\frac{\text{Number of favorable outcomes for a multiple of 3}}{\text{Total number of favorable outcomes}}$

$\text{Probability}=\frac{4}{12}$

$\text{Probability}=\frac{1}{3}$

Now we have to calculate the probability that the result is a multiple of 4.

Favorable outcomes for a multiple of 4 are, 4, 8, 12

Number of favorable outcomes for a multiple of 4 = 3

Total number of outcomes = 12

$\text{Probability}=\frac{\text{Number of favorable outcomes for a multiple of 3}}{\text{Total number of favorable outcomes}}$

$\text{Probability}=\frac{3}{12}$

$\text{Probability}=\frac{1}{4}$

Therefore, the probability for a multiple of 3 or a multiple of 4 is, $\frac{1}{3}$ and $\frac{1}{4}$ respectively.