What is the probability that a student picked at random took Precalculus, given that she passed Calculus?

Question

A college requires certain students to take Precalculus prior to taking Calculus. Thirty-five percent of students that eventually take Calculus take the Precalculus course. Sixty percent of those students that have taken Precalculus pass the Calculus course. Only twenty percent of those students that don’t take Precalculus pass Calculus.

Answer 1

For this problem you would make a tree diagram:

60% pass Calc

35% took Pre-Calc

40% not pass Calc

Take Calc

20% pass Calc

65% did not take Pre-Calc

80% not pass Calc

Probability took pre-calc given then pass calc = 0.35 * 0.60 = 0.21