If $ A $ and $ B $ are two events of a random experiment such that $ P(A \cup B) = 0.65 $ and $ P(A \cap B) = 0.15 $, then $ P(A) + P(B) = ?$
Show Hint
The probability of the union of two events can be found using the formula \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \). Make sure to substitute the given values and solve accordingly.
Step 1: We are given the following information:
\[
P(A \cup B) = 0.65 \quad \text{and} \quad P(A \cap B) = 0.15
\]
The formula for the probability of the union of two events \( A \) and \( B \) is:
\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]
Step 2: Substitute the known values into the formula:
\[
0.65 = P(A) + P(B) - 0.15
\]
Step 3: Solve for \( P(A) + P(B) \):
\[
P(A) + P(B) = 0.65 + 0.15 = 1.2
\]
Thus, the value of \( P(A) + P(B) \) is 1.2.
