The problem asks for the probability that event $A$ or $B$ will occur, represented as $P(A \cup B)$. This is the probability of the union of events $A$ and $B$.

From the Venn diagram in the image, the probabilities associated with each part of the events are:

• Probability of event $A$ alone: $\frac{4}{15}$
• Probability of event $B$ alone: $\frac{2}{15}$
• Probability of the intersection of events $A$ and $B$ (i.e., $A \cap B$): $\frac{2}{15}$

The formula for the union of two events is:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Now, using the values from the diagram:

$P(A \cup B) = \frac{7}{15} + \frac{4}{15} - \frac{2}{15}$

Let me calculate that.The probability that event $A$ or $B$ will occur is $P(A \cup B) = 0.6$, or $\frac{6}{10}$ or 60%.

Would you like further details on this or have any questions?

Here are five related questions to deepen your understanding:

1. What is the difference between independent and mutually exclusive events?
2. How would you calculate the probability if events $A$ and $B$ were mutually exclusive?
3. What is the probability of $A \cap B$ based on the diagram?
4. How does the formula for the union of three events differ from the formula for two events?
5. Can the probability of $P(A \cup B)$ ever be greater than 1?

Tip: For overlapping events like these, always remember to subtract the intersection to avoid double-counting shared outcomes.