28, 56, 84
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- Question:** A statistician is analyzing a discrete uniform distribution over integers from 1 to 84. What is the probability that a randomly selected integer from this range is a multiple of both 7 and 4?
- Solution:** A number divisible by both 7 and 4 must be divisible by \( \text{lcm}(7, 4) = 28 \).
- Find how many multiples of 28 are in \( \{1, 2, \dots, 84\} \):
- These are \( 28 \cdot 1, 28 \cdot 2, 28 \cdot 3 \), so there are 3 such numbers.
- Total integers from 1 to 84: 84.
- \frac{3}{84} = \frac{1}{28}
