Final answer:
To find the probability that a number chosen at random from the set (x: 4 ≤ x ≤ 15) is a multiple of 3 or a multiple of 4, we need to determine the number of multiples of 3 and 4 in the set and then calculate the probability.
Step-by-step explanation:
To find the probability that a number chosen at random from the set (x: 4 ≤ x ≤ 15) is a multiple of 3 or a multiple of 4, we need to determine the number of multiples of 3 and 4 in the set and then calculate the probability.
We can start by finding the number of multiples of 3. The multiples of 3 in the set are 6, 9, 12, and 15. So, there are 4 multiples of 3.
Next, let's find the number of multiples of 4. The multiples of 4 in the set are 4, 8, and 12. So, there are 3 multiples of 4.
Now, we need to find the total number of elements in the set. The set (x: 4 ≤ x ≤ 15) contains the numbers 4, 5, 6, ..., 15. So, there are 15 - 4 + 1 = 12 elements in the set.
To calculate the probability, we add the number of multiples of 3 and 4 and divide by the total number of elements in the set:
Probability = (Number of multiples of 3 + Number of multiples of 4) / Total number of elements = (4 + 3) / 12 = 7/12