Dependent and Independent Probability Question, please help.

Question

1.Brian has examinations coming up in calculus and biology. He estimates that his odds in favour of passing the calculus examination are 17:3 and his odds against passing the biology examination are 3:7. Assume these to be independent events.

a) What is the probability that Brian will pass both exams?

b) What are the odds in favour of Brian failing both exams?

c) What factors could make these two events dependent?

Answer 1

17:3 odds translates to 17/20 probability pass and 3/20 probability fail

3:7 odds translates to 3/10 probability fail and 7/10 probability pass

a) probability pass both: 17/20 * 7/10 = 119/200

b) probability fail both: 3/20 * 3/10 = 9/200 --> 9:191 odds

c) If the performance on one exam are connected in any way to the other exam.