



 
Hi Sandy, In the problem you mention the student is instructed to use a diagram so let's do it that way. Here is how I would start. I am going to assume there are 100 students in the class so I can deal with counts rather than percentages. You are told there are 80 students in the orange circle, 60 students in the blue circle but all together there are only 90 students who use either the internet or email. 80 + 60 = 140 and 140  90 = 50 so 50 of the students got counted twice. These are the students in the overlap of the two circles so now you can see how the 90 students are arranged, 80 students in the internet circle, 60 in the email circle and 90 students in total. The question asked is "Determine the probability that the student used email, given that the student used the internet for school projects." The clause "given that the student used the internet for school projects" tells you that you need to focus on the internet circle. There are 80 students in this circle and you want the probability that if you select one of them then the student you select also uses email. 50 of the students in this circle use email so the probability is 50/80 = 5/8. I like this solution since the diagrams really help me see what is going on. You can however solve the problem just using formulas. If E represents the students who use email and I represents the students who use the internet then
You know P(I or E) = 0.90, P(I) = 0.80 and P(E) = 0.60 so
so
The probability that the student used email, given that the student used the internet for school projects is
If this were my class I would show the students both techniques. I hope this helps,  


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