The probability of choosing a number from set A union B is 12 unique elements divided by the 19 total elements in the universal set, resulting in approximately 0.6316, or 63.16%.
When we want to find the probability of a number being in set A union B, we need to consider all unique elements in both sets without double counting any element that might be in both. Given the universal set S includes numbers 1 through 29, and set A and B are defined as:
A = {2, 4, 6, 8, 10, 12, 14, 16, 18}
B = {14, 15, 16, 17, 18, 19}
We identify the unique elements in the union of A and B, which are {2, 4, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19}. We count these to find there are a total of 12 unique outcomes in A union B the universal set has 19 outcomes.
Therefore, the probability you will choose a number from A union B is the number of unique outcomes in A union B divided by the number of outcomes in S.
The formula is:
P(A union B) = number of outcomes in A union B / number of outcomes in S
So: P(A union B) = 12 / 19 ≈ 0.6316
Thus, the probability is approximately 0.6316, or 63.16%.
The question probable may be:
What is the probability of choosing a number from the union of sets A and B, given the defined sets and universal set, and how is this probability calculated?