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Probability Confusion

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Why bother with a post grad course - waste of time? 17-10-2016
1. Hey all,

I'm having a bit of trouble understanding probability.

So I came across this data with a question:

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)
2. 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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Updated: October 16, 2016
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