# Help with the problem of conditional probability

Two friends are students of the subject of Statistics so that when one passes the notes lack other. It is known that the first will attend 80% of classes and the second at 40%, independently. What is the probability that the friends have all class notes?

• How many classes? Jul 18 '13 at 5:08

For any particular class, let $A'$ be the event "Alicia did not attend," and $B'$ be the event "Beti did not attend." The probability of $A'$ is $0.2$, and the probability of $B'$ is $0.6$. Thus by independence the probability neither showed up is $0.12$.
It follows that with probability $0.88$ at least one showed up, so they have the notes for that class.
If there are $n$ classes, the probability they have all the notes is $(0.88)^n$. Here we are assuming that attending the various classes are independent events. This is probably not a reasonable assumption.
Remark: Or else let $A$ be the even Alicia attended, and $B$ be the event Beti did. Then $\Pr(A\cap B)=0.32$. Now use the formula $\Pr(A\cup B)=\Pr(A)+\Pr(B)-\Pr(A\cap B)$ to conclude that $\Pr(A\cup B)=0.88$. So the probability one or both attended is $0.88$.