100 homeworks are on the table, with two questions to be graded on each homework

Question

100 homeworks are on the table, with two questions to be graded on each homework. Aditya is in charge of grading question one and Jingjing is in charge of grading question two. First, Aditya grades some homeworks at random; each homework has probability 0.3 of being graded. Next, Jingjing randomly grades half of the homeworks. That is, he grades 50 homeworks. Assume Aditya and Jingjing make their choices independently

1. Let N be the number of homeworks that Aditya graded. What is E[N]?

2. Let M be the number of homeworks that Aditya graded and Jingjing did not grade. What is E[M]?

Explanation / Answer

1) As E(N) =np where n=100 and p=0.3

=100*0.3=50

2) probabilty that a homework graded by Aditya and does not graded by Jingjing =0.3*0.5=0.15

hence E(M)=100*0.15=15

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