Question: Refer to the Venn diagram to the right for events A and B in an equally likely sample space S. Find…

Refer to the Venn diagram to the right for events A and B in an equally likely sample space S. Find the indicated probability. S P((A∩B)’) 45 15 25 15 P((A∩B)’) = (Type a decimal.) Clear all

Solution

To solve the problem, we need to find the probability of the complement of the intersection of events A and B, denoted as \( P((A \cap B)’) \). Step 1: Identify the relevant numbers from the Venn diagram. - The number of elements in \( A \cap B \) is 15. - The total number of elements in the sample space \( S \) is the sum of all elements in the Venn diagram: \( 45 + 25 + 15 + 15 = 100 \). Step 2: Calculate the probability of the intersection \( A \cap B \). \[ P(A \cap B) = \frac{15}{100} \] Step 3: Calculate the complement probability \( P((A \cap B)’) \). \[ P((A \cap B)’) = 1 - P(A \cap B) \] Step 4: Substitute the value from Step 2 into the equation in Step 3. \[ P((A \cap B)’) = 1 - \frac{15}{100} = 1 - 0.15 = 0.85 \] Thus, the probability \( P((A \cap B)’) \) is 0.85.