Question 1005150
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p = pepperoni
o = olives

P(p) = 0.7 means that 7 out of 10 people like p OR p & o.  Similarly, P(o) = 0.6 means that 6 out of 10 people like o OR p & o. P(p OR o) = 0.8 means that 8 out of 10 people like p OR o OR p & o.


If you add 0.7 and 0.6, you get 1.3 which is greater than 1.  Therefore, adding these two values have caused us to count something twice, and that thing we have counted twice is P(p & o).  Why?  Read on.


P(p) = P(p & ~o) + P(p & o)


P(o) = P(o & ~p) + P(p & o)


P(p OR o) = P(p & ~o) + P(o & ~p) + P(p & o)


P(p) + P(o) =  P(p & ~o) + P(p & o) + P(o & ~p) + P(p & o)


P(p) + P(o) - P(p OR o) = P(p & o)


0.7 + 0.6 - 0.8 = 0.5


*[illustration Pepp_Olives_Venn.jpg]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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