Question

i need help with both but its fine if you cant

Answer 1

The conditional probability is given by:

$P(B|A)=\frac{P(A\cap B)}{P(A)}$

Let A be the event "the student is male" and B the event "First class is humanities".

The probability of A is:

$P(A)=\frac{215}{380}$

The probability of event A and B is:

$P(A\cap B)=\frac{50}{380}$

Therefore the conditional probability is:

$P(B|A)=\frac{\frac{50}{380}}{\frac{215}{380}}=\frac{50}{215}=\frac{10}{43}$

Therefore the probability we are looking for is 10/43