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

To find \( P(A \cup B) \), we can use the formula of probability for the union of two events: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).

First, we need to find \( P(A \cap B) \), which is the intersection of events \( A \) and \( B \).

We use the conditional probability formula: \( P(A \cap B) = P(A | B) \cdot P(B) \).

Given \( P(A | B) = 0.6 \) and \( P(B) = 0.8 \), we compute \( P(A \cap B) \) as follows:

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

Now we can find \( P(A \cup B) \):

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

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

Therefore, the correct answer is 0.72.

Answer 2

The formula for the union of two events is:

\( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).

The conditional probability \( P(A \mid B) \) is related to \( P(A \cap B) \) as:

\( P(A \cap B) = P(A \mid B) \cdot P(B) \).

Substitute the given values:

\( P(A \cap B) = (0.6)(0.8) = 0.48 \).

Now calculate \( P(A \cup B) \):

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

Thus, the probability \( P(A \cup B) \) is 0.72.