Venn Diagram question for Statistics?

So this is the question in our Chapter 3 homework assignment for my online AP Stat class.





60 employees from a company was surveyed. Of the 60, 40 had college degrees, 10 were single, and 6 were single college graduates. The probability that an employee of the company is single or has a college degree is:


A. 0.10


B. 0.25


C. 0.667


D. 0.733





I think it's D. So this is how I did it. There is an overall rectangle and 2 circles in the center. The left circle has 34, the right has 4, the middle has 6, and the outside has 16. I added 34+6+4 and divided it all by 60 and got 0.733. Did I do it right?

Venn Diagram question for Statistics?
Hi,





Your logic and your answer are perfect!!





Good work!! :-)
Reply:*thumbs up*





Another way we could do it is by using the following (called the inclusion-exclusion principle):


#(single or college) = #(single) + #(college) - #(single and college)


= 10 + 40 - 6


= 44


And then dividing 44/60 to get .73333, again giving us D.





Though unless the problem gets more difficult, your way is perfectly fine.
Reply:Yes you are absolutely correct.


Here n(S) = 60


n(College) = 40


n(Single) = 10


n(College intersection Single) = 6


As per law, n(College U Single) = n(College) + n(Single) - n(College intersection Single)


= 40 + 10 - 6


= 44


And probability = 44/60 = 0.7333333333.
Reply:I just finished my AP Stats class... and I struggled, quite a lot. If this is summer homework, my advice to you is to do ALL your homework throughout the course, because it can get overwhelming if you miss something.





This might help... the key word in this question is OR. That means you're going to have to take into account the probability of an employee being single, the probability of them having a degree, and both, I believe... which it looks like you did. I don't remember exactly, but you may want to multiply the probability of ALLL THREE together to get your answer.... but that may have been a method way later in the book, so... try it, and if it seems way off, then it probably is, haha. Like I said, I struggled, but one thing I learned is that you have to try a couple things and see what looks right.





Did you check the back of the book?