Suppose that the probability that your alarm goes off in the morning is 0.9. If the alarm goes off, the probability is 0.8 that you attend your 8 a.m. class. If the alarm does not go to off, the probability that you make your 8 a.m.class is 0.5. Find the probability that you make your 8 a.m. class.

Explanation

Let A be the event thet my alarm goes off and let B be the event that I make my 8 a.m. class.
Since S = `a cup A., B=(B cap A) cup (B cap A.)` Where B cap A and B cap A, are mutually exclusive events. `therefore P(B)=P(B cap A)+P(B cap A.)`
`=P(A). P(B/A)+P(A.). P(B/A.)`
`=0.9xx0.8+0.1xx0.5=0.77`