double expectation example

Q) There are 2 types of actuarial students, smart and not-so-bright. THe bright one pass 80% of exams they take and no-so-bright pass 40% of exams they take. All studnets start with Exam 1 and take the exams in sequence, and drop out as soon as they fail one exam. An equal number of bright and not-so-bright students take Exam 1. Debermine the probabilty of randomly selected student taking Exam 3 will pass.



A) I don't understand a part of ASM solution where they approach as following:

P(Passing|Taking Exam 3)=P(Passing|Bright &Taking Exam3) x P(Bright | Taking Exam3) + P(Passing | NotBright & Taking exam 3) x P(Not Bright | Taking Exam3).



Can someone help me to understand this?



Thanks

double expectation example