Question

If \( P(A) = 0.4 \), \( P(B) = 0.8 \) and \( P(A | B) = 0.6 \), then \( P(A \cup B) \) is:

• A. 0.96
• B. 0.72
• C. 0.36
• D. 0.42

Answer 1

The Correct Option is B

The probability of the union of two events, \( P(A \cup B) \), is calculated using the formula \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).

To proceed, we first determine the probability of the intersection of events \( A \) and \( B \), denoted as \( P(A \cap B) \).

The conditional probability formula is applied here: \( P(A \cap B) = P(A | B) \cdot P(B) \).

With the given values \( P(A | B) = 0.6 \) and \( P(B) = 0.8 \), the calculation for \( P(A \cap B) \) is:

\[ P(A \cap B) = 0.6 \times 0.8 = 0.48 \]

Now, we can compute \( P(A \cup B) \):

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

\[ P(A \cup B) = 0.4 + 0.8 - 0.48 = 0.72 \]

The final result is 0.72.