Two students John and Mary are both registered for the same

Two students, John and Mary, are both registered for the same course. If John attends 80 percent of the time and Mary 60 percent (and their attendance patterns are totally independent), then if at least one of John or Mary are in attendance on a given day, what is the probability that it is John?

Solution

P(at least one of John or Mary are in attendance) = 1 - both absent
= 1-(0.2*0.4)
= 0.92

John present = 0.80

so,
P(John present given at least one of John or Mary are in attendance) = 0.8/0.92 = 20/23 = 0.8696