A and B are two events such that `P(A)=0.60, P(A"or"B)=0.85` and `P` (A and B`=0.42`, then find `P(B)`.

Explanation

To find \( P(B) \), we can use the formula for the probability of the union of two events:

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

Given:
- \( P(A) = 0.60 \)
- \( P(A \cup B) = 0.85 \)
- \( P(A \cap B) = 0.42 \)

We can substitute these values into the formula:

\[ 0.85 = 0.60 + P(B) - 0.42 \]

Now, we can simplify the equation:

1. Combine the known probabilities on the right side:
\[ 0.85 = 0.60 - 0.42 + P(B) \]
\[ 0.85 = 0.18 + P(B) \]

2. Now, isolate \( P(B) \):
\[ P(B) = 0.85 - 0.18 \]
\[ P(B) = 0.67 \]

Thus, the probability \( P(B) \) is \( 0.67 \).