The probability that A can solve a problem is `2//3` and B can solve it is `3//4`. If both attempt the problem, what is the probability that the problem gets solved ?

Options

A. `11//12`
B. `7//12`
C. `5//12`
D. `9//12`

Answer

To find the probability that the problem gets solved when both A and B attempt it, we can follow these steps:

### Step 1: Identify the probabilities
Let:
- \( P(A) \) = Probability that A can solve the problem = \( \frac{2}{3} \)
- \( P(B) \) = Probability that B can solve the problem = \( \frac{3}{4} \)

### Step 2: Calculate the probabilities of not solving the problem
- The probability that A does not solve the problem, \( P(A') \) = \( 1 - P(A) = 1 - \frac{2}{3} = \frac{1}{3} \)
- The probability that B does not solve the problem, \( P(B') \) = \( 1 - P(B) = 1 - \frac{3}{4} = \frac{1}{4} \)

### Step 3: Calculate the probability that neither A nor B solves the problem
The probability that both A and B do not solve the problem is given by:
\[ P(A' \cap B') = P(A') \times P(B') = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12} \]

### Step 4: Calculate the probability that at least one of them solves the problem
The probability that the problem gets solved (at least one of them solves it) is:
\[ P(\text{Solved}) = 1 - P(A' \cap B') = 1 - \frac{1}{12} = \frac{12}{12} - \frac{1}{12} = \frac{11}{12} \]

### Conclusion
The probability that the problem gets solved when both A and B attempt it is \( \frac{11}{12} \).