Help!!! I'm not really good at Bayes' Theorem. Can you please walk me through.

In the current second year class of a top ranked US university, all students come from three states in the US . Kansas, Illinois, and Ohio supply respectively 40%, 50%, and 10% of the students. The failure rate of students is 4%, 2%, and 6% respectively.

What is the probability that a student chosen at random will fail?
Given that a student fails , what is the probability that he or she came form Kansas?

say 100 students

40 from Ka .04*40 = 1.6 fails
50 from Ill .02 * 50 = 1 fails
10 from Oh .06 * 10 = .6 fails

total failures = 1.6+1+.6 = 3.2
That is 3.2/100 = 3.2 % = .032

3.2 fail, 1.6 of whom are from Ka
1.6/3.2 = .5 or 50%

BUT you said use Bayes so
P(Ka if failed) =P(failed if Ka)P(Ka)/P(fail)

= .04 ( .4/.032) = .5 whew, that had me worried :)