**Mutually Exclusive Events**

Mutually exclusive events are events that cannot occur simultaneously. In other words, if event A happens, then event B cannot happen, and vice versa. Mathematically, we can represent this as:

P(A ∩ B) = 0

where P(A ∩ B) represents the probability of both events A and B occurring together.

**Probability of Event A and Event B**

Given that event A has a probability of P(A) = 3 and event B has a probability of P(B) = 4, we need to find the probability of the union of events A and B, denoted as P(A ∪ B).

**Probability of Union of Mutually Exclusive Events**

When two events are mutually exclusive, the probability of their union is simply the sum of their individual probabilities. Mathematically, we can represent this as:

P(A ∪ B) = P(A) + P(B)

This formula holds true when A and B are mutually exclusive. Since we are given that A and B are mutually exclusive, we can use this formula to find P(A ∪ B).

**Calculation:**

P(A ∪ B) = P(A) + P(B)
P(A ∪ B) = 3 + 4
P(A ∪ B) = 7

Therefore, the probability of the union of events A and B is 7.

**Explanation:**

The reason why the formula P(A ∪ B) = P(A) + P(B) holds true for mutually exclusive events is that when two events cannot occur at the same time, there is no overlap between their outcomes. So, the probability of their union is simply the sum of their individual probabilities. In this case, since A and B are mutually exclusive, the probability of A ∪ B is the sum of P(A) and P(B).

To better understand this concept, let's consider a simple example. Suppose event A is rolling an odd number on a fair six-sided die, and event B is rolling an even number on the same die. Since an odd number and an even number cannot occur simultaneously, these events are mutually exclusive. The probability of rolling an odd number (P(A)) is 3/6 = 1/2, and the probability of rolling an even number (P(B)) is also 3/6 = 1/2. The probability of rolling either an odd number or an even number (P(A ∪ B)) is the sum of these probabilities, which is 1/2 + 1/2 = 1.

In conclusion, when two events are mutually exclusive, the probability of their union is the sum of their individual probabilities. In the given scenario, since A and B are mutually exclusive events with probabilities of 3 and 4, respectively, the probability of their union is 7.