The probability of the occurrence of event A is `1/3` and the probability of the occurrence of event B is `1/4`. Find the probability that neigher A nor B will occur, it is given that A and B are mutually exclusive events.

Explanation

To find the probability that neither event A nor event B will occur, we can follow these steps:

### Step 1: Identify the probabilities of events A and B
Given:
- Probability of event A, \( P(A) = \frac{1}{3} \)
- Probability of event B, \( P(B) = \frac{1}{4} \)

### Step 2: Calculate the probability of either event A or event B occurring
Since events A and B are mutually exclusive, the probability of either A or B occurring is the sum of their individual probabilities:
\[ P(A \cup B) = P(A) + P(B) = \frac{1}{3} + \frac{1}{4} \]

### Step 3: Find a common denominator to add the fractions
The least common multiple of 3 and 4 is 12. We convert the fractions:
\[ P(A) = \frac{1}{3} = \frac{4}{12} \]
\[ P(B) = \frac{1}{4} = \frac{3}{12} \]

Now, we can add them:
\[ P(A \cup B) = \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \]

### Step 4: Calculate the probability that neither A nor B occurs
The probability that neither A nor B occurs is given by:
\[ P(\text{neither A nor B}) = 1 - P(A \cup B) \]
Substituting the value we found:
\[ P(\text{neither A nor B}) = 1 - \frac{7}{12} \]

### Step 5: Simplify the expression
To perform the subtraction:
\[ 1 = \frac{12}{12} \]
Thus,
\[ P(\text{neither A nor B}) = \frac{12}{12} - \frac{7}{12} = \frac{5}{12} \]

### Conclusion
The probability that neither event A nor event B will occur is:
\[ \boxed{\frac{5}{12}} \]

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