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 \( P(B) \) given the probabilities of events A and B, we can use the formula for the probability of the union of two events:

\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]

### Step-by-Step Solution:

1. **Write down the given probabilities:**
- \( P(A) = 0.60 \)
- \( P(A \text{ or } B) = 0.85 \)
- \( P(A \text{ and } B) = 0.42 \)

2. **Substitute the known values into the formula:**
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
becomes:
\[ 0.85 = 0.60 + P(B) - 0.42 \]

3. **Rearrange the equation to solve for \( P(B) \):**
\[ 0.85 = 0.60 + P(B) - 0.42 \]
Simplifying the right side:
\[ 0.85 = 0.60 - 0.42 + P(B) \]
\[ 0.85 = 0.18 + P(B) \]

4. **Isolate \( P(B) \):**
\[ P(B) = 0.85 - 0.18 \]
\[ P(B) = 0.67 \]

5. **Final answer:**
Thus, the probability of event B is:
\[ P(B) = 0.67 \]