from the sample space $\mathrm{S}$ $=\{1,2,3,4, \ldots, 15\}$, a single number is to be selected at random. given the following events, find the indicated probability. A. the selected number is even. B. The selected number is a multiple of 4 . C. The selected number is a prime number. $P(A$ and $B)$
Solution
Step 1 ：Define the sample space S = {1,2,3,4,...,15}, from which a single number is to be selected at random.
Step 2 ：Identify the events: A. the selected number is even, B. The selected number is a multiple of 4.
Step 3 ：Determine the total number of outcomes in the sample space, which is 15.
Step 4 ：Identify the numbers in the set that are both even and a multiple of 4. These are 4, 8, and 12. So, there are 3 favorable outcomes.
Step 5 ：Calculate the probability of selecting a number that is both even and a multiple of 4 by dividing the number of favorable outcomes by the total number of outcomes in the sample space. This gives \( \frac{3}{15} = 0.2 \).
Step 6 ：Final Answer: The probability of selecting a number that is both even and a multiple of 4 from the set {1,2,3,4,...,15} is \( \boxed{0.2} \).
