A salesman has a 70% change to sell a product to any customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A and B?

Options

A. 0.98
B. 0.91
C. 0.7
D. 0.49

Answer

To solve the problem, we need to find the probability that the salesman sells the product to both customers A and B.

### Step-by-Step Solution:

1. **Identify the Probability of Selling to One Customer**:
The problem states that the salesman has a 70% chance of selling the product to any customer. We can express this probability as:
\[ P(A) = 0.7 \quad \text{(Probability of selling to customer A)} \]
\[ P(B) = 0.7 \quad \text{(Probability of selling to customer B)} \]

2. **Use the Independence of Events**:
Since the behavior of successive customers is independent, the probability of selling to both customers A and B can be calculated by multiplying their individual probabilities:
\[ P(A \text{ and } B) = P(A) \times P(B) \]

3. **Calculate the Combined Probability**:
Substituting the values we have:
\[ P(A \text{ and } B) = 0.7 \times 0.7 \]
\[ P(A \text{ and } B) = 0.49 \]

4. **Conclusion**:
Therefore, the probability that the salesman will sell the product to both customers A and B is:
\[ P(A \text{ and } B) = 0.49 \quad \text{or} \quad 49\% \]