Probability Confusion

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    Hey all,

    I'm having a bit of trouble understanding probability.

    So I came across this data with a question:

    Name:  2016-10-16 05_11_20-Microsoft Word - Tutorial Week 3-Questions.docx.png
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    The question is:

    "Calculate the probability that a randomly selected shareholder owns fewer than 200 shares or is against the merger."

    Now I thought that I could just add the 12,3,10 and 6 together to get 31, therefore the probability would be 31/50.

    I then decided that since I knew the answer I would try using the formula: "p(a)+p(b)-p(a∩b)" to get the same answer, however, this was not the case. Instead, I ended up getting 19/50+15/50 - (19/50x15/50) = 283/500

    Obviously, these are different answers so... Which one is correct and where did I go wrong with the other?

    Thanks.

    (Also, sorry for making this so long, I wanted this to be fairly detailed so you could see my steps and thought process)
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    The problem with the second method is the working out of P(A and B). P(A and B) = P(A) x P(B) is only true for independent events.
 
 
 
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