Question

At a certain university, the likelihood of a student passing Electromagnetics is 43%. However, if the student has already passed Signals and Systems, this likelihood increases to 64%. Assuming that the likelihood of passing Signals and Systems is 58%, what is the likelihood of passing both classes?

Answer 1

We are given here that:
P( passing electromagnetics ) = 0.43,

Also, we are given here that:
P( passing electromagnetics | passed Signals and Systems) = 0.64

Also, we are given here that:
P( passed Signals and Systems) = 0.58

The probability of passing both is computed using Bayes theorem here as:
P( passed both ) = P( passing electromagnetics | passed Signals and Systems) P( passed Signals and Systems)

P(passed both) = 0.58*0.64 = 0.3712

Therefore 0.3712 is the required probability here.