A and B are two events such that `P(A)=0.5, P(B)=0.4` and `(A "or"B)=0.6`, then find `P(A "and"B)`.

Explanation

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

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

Given:
- \( P(A) = 0.5 \)
- \( P(B) = 0.4 \)
- \( P(A \text{ or } B) = 0.6 \)

We can rearrange the formula to solve for \( P(A \text{ and } B) \):

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

Now, substitute the given values into the equation:

\[ P(A \text{ and } B) = 0.5 + 0.4 - 0.6 \]

Calculating the right-hand side:

\[ P(A \text{ and } B) = 0.9 - 0.6 = 0.3 \]

Thus, the probability of both events A and B occurring is:

\[ P(A \text{ and } B) = 0.3 \]