Question

use the following venn diagram to determine the probability of the given event. provide an answer in fraction form.
p(b ∩ a)

Explanation:

Step1: Find \( n(B \cap A) \)

The region for \( B \cap A \) includes the parts where circles A and B overlap. From the Venn diagram, this is \( 8 + 3 = 11 \).

Step2: Find \( n(A) \)

The region for A includes all parts of circle A: \( 17 + 8 + 3 + 5 = 33 \).

Step3: Calculate \( P(B|A) \)

Using the formula \( P(B|A) = \frac{n(B \cap A)}{n(A)} \), substitute the values: \( \frac{11}{33} = \frac{1}{3} \).

Answer:

\(\frac{1}{3}\)