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?
2026-04-13 07:50:13.1776066613
Help with the problem of conditional probability
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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 $0.88$.