Rounded to the two decimals, determine P(Sophomore | Off-Campus).

Question

Imagine a diagram. In the left circle its labeled 0.22 for sophomores. In the right circle its labeled 0.10 for off-campus. In the middle circle its labeled 0.06

Answer 1

This question asks you to visualize a venn diagram with probabilities. It gives you P(Sophomores) as 0.22, P(Off-campus) as 0.10, and the P(Both) as 0.06. All we have to do here is use the formula for a given event and plug our values in.

P(B|A) = P(Both) / P(A)

So, in this case we would have that:

P(Sophomore|Off-campus) = P(Both) / P(Off-campus)

These values are given to us, so we'll just plug them in and solve:

P(Sophomore|Off-campus) = 0.06 / 0.10 = 0.60

So the probability that the student is a sophomore given that they live off-campus is 0.60