Answer:
![\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
Given that, spinner has 12 equal areas, so there are 12 possibilities of occurrences i.e. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Multiples of 3 are: {3, 6, 9, 12}
Multiples of 4 are: {4, 8, 12}
To find the multiple of 3 or 4, we need to find the union of the above two sets.
Multiples of 3 or 4: {3, 4, 6, 8, 9, 12}
Number of multiples of 3 or 4 = 6
Formula for probability of an event E can be observed as:
![P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cdfrac%7B%5Ctext%7BNumber%20of%20favorable%20cases%7D%7D%7B%5Ctext%20%7BTotal%20number%20of%20cases%7D%7D)
Here, number of favorable cases are 6 and
Total number of cases are 12.
Therefore the required probability is:
![P(\text{Multiple of 3 or 4}) = \dfrac{6}{12}\\P(\text{Multiple of 3 or 4}) = \bold{\dfrac{1}{2}}](https://tex.z-dn.net/?f=P%28%5Ctext%7BMultiple%20of%203%20or%204%7D%29%20%3D%20%5Cdfrac%7B6%7D%7B12%7D%5C%5CP%28%5Ctext%7BMultiple%20of%203%20or%204%7D%29%20%3D%20%5Cbold%7B%5Cdfrac%7B1%7D%7B2%7D%7D)