Question

The probability of a student taking both Spanish class and art class is 9/100 . The probability of a student taking art class is 3/10
What is the probability that a student takes Spanish class given that the student takes art class?

Answer 1

Denote by A the event "taking  Spanish class "
B the event "student taking art class"
We have the formula: $P(A!B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{9}{100}}{\frac{3}{10}}\\=\frac{9}{100}\times\frac{10}{3}=\frac{3}{10}$
Answer $\frac{3}{10}$