To find the probability of A or B occurring, we use the formula for the union of two events:

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

Step 1: Identify values from the diagram

• $P(A) = \frac{2}{15} + \frac{7}{15} = \frac{9}{15}$
• $P(B) = \frac{7}{15} + \frac{4}{15} = \frac{11}{15}$
• $P(A \cap B) = \frac{7}{15}$

Step 2: Apply the formula

$P(A \cup B) = \frac{9}{15} + \frac{11}{15} - \frac{7}{15}$

Step 3: Simplify the expression

$P(A \cup B) = \frac{9 + 11 - 7}{15} = \frac{13}{15}$

Final Answer

$P(A \cup B) = \frac{13}{15}$

Would you like further clarification or a detailed breakdown of any step?

5 Related Questions:

1. What is the formula for the union of three events, $A \cup B \cup C$?
2. How does the concept of mutually exclusive events affect this type of calculation?
3. Can the union formula be extended to events with dependent probabilities?
4. How do we calculate $P(A \cap B^c)$ for the complement of B?
5. What does it mean if $P(A \cap B) = 0$?

Tip:

Always double-check if events are independent or mutually exclusive before applying standard probability formulas!