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The Venn diagram in the image represents two mutually exclusive events, \( A \) and \( B \), where the probabilities are given. Mutually exclusive events mean that the events cannot happen at the same time, implying that their intersection is zero.

### Given:
- Probability of event \( B \) is 0.4.
- The probability of neither event \( A \) nor event \( B \) happening is 0.2.
- The total probability must sum to 1.

### Let the probability of event \( A \) be \( y \).

The total probability formula is:

\[
P(A) + P(B) + P(\text{neither A nor B}) = 1
\]

Substituting the known values:

\[
y + 0.4 + 0.2 = 1
\]

Solving for \( y \):

\[
y = 1 - 0.6 = 0.4
\]

### Therefore, the value of \( y \) is 0.4.

Would you like further details or explanations on this? Here are some related questions:

1. How do mutually exclusive events affect probability calculations?
2. What would happen if the events were not mutually exclusive?
3. How is the total probability rule applied to more than two events?
4. What is the relationship between independent and mutually exclusive events?
5. Can you explain the difference between disjoint and overlapping events?

**Tip:** When working with probabilities, always ensure that the sum of all possible outcomes equals 1.

The Venn diagram below illustrates the mutually exclusive events. The values on the diagram represent probabilities. Find the value of y.

Explore how to find the probability of a mutually exclusive event using a Venn diagram. This problem involves calculating the probability of event A and event B with given probabilities, using the total probability formula. Suitable for students in Grades 10-12.

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