The probability of solving a question by jindal is 3/5 while that of not solving it by Avi `1//4` What is the probability that the problem be solved?

Options

A. A)`(3)/(5)`
B. B)`(7)/(10)`
C. C)`(1)/(5)`
D. D)`(9)/(10)`

Answer

To solve the problem, we need to find the probability that the question is solved by either Jindal or Avi. We will first determine the probabilities of each person solving the question, then find the probability that neither of them solves it, and finally calculate the probability that at least one of them solves it.

### Step-by-Step Solution:

1. **Identify the probabilities:**
- The probability of Jindal solving the question, \( P(J) = \frac{3}{5} \).
- The probability of Avi not solving the question, \( P(A') = \frac{1}{4} \).

2. **Calculate the probability of Avi solving the question:**
- The probability of Avi solving the question, \( P(A) = 1 - P(A') = 1 - \frac{1}{4} = \frac{3}{4} \).

3. **Calculate the probability of Jindal not solving the question:**
- The probability of Jindal not solving the question, \( P(J') = 1 - P(J) = 1 - \frac{3}{5} = \frac{2}{5} \).

4. **Calculate the probability that both Jindal and Avi do not solve the question:**
- The combined probability of both not solving the question is given by:
\[ P(J' \cap A') = P(J') \times P(A') = \frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10}. \]

5. **Calculate the probability that at least one of them solves the question:**
- The probability that at least one of them solves the question is:
\[ P(J \cup A) = 1 - P(J' \cap A') = 1 - \frac{1}{10} = \frac{9}{10}. \]

6. **Conclusion:**
- Therefore, the probability that the problem is solved is \( \frac{9}{10} \).

### Final Answer:
The probability that the problem is solved is \( \frac{9}{10} \).

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