Probability/Algebra 2 (PLEASE HELP)

Question

James can attend either Irvine Valley College or Golden West College this summer for a class. If James attends Irvine Valley College, he is 70% likely to take Philosophy and 30% likely to take Music Appreciation. If he attends Golden West College, he is 40% likely to take Astronomy and 60% likely to take Chemistry. Overall, James has a 20% likelihood of taking Astronomy. What is James’s overall likelihood of taking Philosophy this summer?

Answer 1

I think what is being asked here is to find the probability of attending either school.

100p% for IV and 100(1-p)% for GW.

Then (1-p)*.4=.2 for attending astronomy at GW => p=.5

Then .5*.7=.35 = probability of philosophy