Question

find the probability that event a or b will occur.
a: $\frac{4}{15}$, b: $\frac{7}{15}$
$p(a \text{ or } b) =?$

Explanation:

Step1: Identify the formula for mutually exclusive events

For mutually exclusive events (no overlap), \( P(A \text{ or } B) = P(A) + P(B) \). From the Venn diagram, events A and B are mutually exclusive (no overlapping region), so we use this formula.

Step2: Substitute the given probabilities

Given \( P(A) = \frac{4}{15} \) and \( P(B) = \frac{7}{15} \). Then \( P(A \text{ or } B) = \frac{4}{15} + \frac{7}{15} \).

Step3: Add the fractions

When adding fractions with the same denominator, we add the numerators: \( \frac{4 + 7}{15} = \frac{11}{15} \).

Answer:

\(\frac{11}{15}\)