Answer: 0.40.

## Explanation Let's define the events: - Let A = event that a portfolio manager reads Business News weekly - Let B = event that a portfolio manager reads BloomField News Given: - P(A) = 0.50 - P(B) = 0.40 - P(A ∩ B) = 0.30 (probability of reading both) We need to find the probability that a portfolio manager does NOT read either newspaper, which is P(A' ∩ B') or 1 - P(A ∪ B). **Step 1: Calculate P(A ∪ B)** Using the addition rule of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) P(A ∪ B) = 0.50 + 0.40 - 0.30 = 0.60 This means the probability that a portfolio manager reads at least one of the two newspapers is 0.60. **Step 2: Calculate the complement** The probability that a portfolio manager does NOT read any of the two newspapers is: P(neither) = 1 - P(A ∪ B) = 1 - 0.60 = 0.40 **Verification using Venn diagram approach:** - Probability of reading only Business News: P(A) - P(A ∩ B) = 0.50 - 0.30 = 0.20 - Probability of reading only BloomField News: P(B) - P(A ∩ B) = 0.40 - 0.30 = 0.10 - Probability of reading both: 0.30 - Total probability of reading at least one: 0.20 + 0.10 + 0.30 = 0.60 - Probability of reading neither: 1 - 0.60 = 0.40 Therefore, the correct answer is **B) 0.40**.

Author: Nikitesh Somanthe