GB-18-06-001 · Conditional probability

Of 57 students, 30 study art, 29 study music and 8 study both. A student who studies art is chosen at random. Find the probability that this student also studies music.

Venn Diagrams: Conditional Probability {B | A} Booklet p. 62

Method

P(B given A) = (Double shaded overlap A ∩ B) / (Total in A)

Worked Example (GB-18-06-001)

Conditioning on art restricts the sample space to the 30 art students.

P(\text{music}\mid\text{art})=\frac{8}{30}=\frac{4}{15}

Ans =

\frac{4}{15}