A can solve 75% of the problems of Mathematics and B can solve 70%. What is the probability that either A or B can solve a problem chosen at random ?

Answer

To solve the problem, we need to find the probability that either A or B can solve a problem chosen at random. We can use the principle of complementary probabilities and the formula for the union of two independent events.

### Step-by-step Solution:

1. **Identify the probabilities of A and B solving a problem:**
- Probability that A can solve a problem, \( P(A) = 0.75 \) (or 75%)
- Probability that B can solve a problem, \( P(B) = 0.70 \) (or 70%)

2. **Calculate the probabilities that A and B cannot solve a problem:**
- Probability that A cannot solve a problem, \( P(A') = 1 - P(A) = 1 - 0.75 = 0.25 \)
- Probability that B cannot solve a problem, \( P(B') = 1 - P(B) = 1 - 0.70 = 0.30 \)

3. **Calculate the probability that neither A nor B can solve the problem:**
- Since A and B are independent events, the probability that both A and B cannot solve the problem is:
\[ P(A' \cap B') = P(A') \times P(B') = 0.25 \times 0.30 = 0.075 \]

4. **Calculate the probability that either A or B can solve the problem:**
- The probability that either A or B can solve the problem is the complement of the probability that neither can solve it:
\[ P(A \cup B) = 1 - P(A' \cap B') = 1 - 0.075 = 0.925 \]

5. **Final Answer:**
- The probability that either A or B can solve a problem chosen at random is \( 0.925 \) or \( 92.5\% \).