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# Probability using venn diagrams

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qualitystreet  Apr 21, 2018
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$$x(x-2)+x+2x+8+10=60\\ x^2-2x+3x+18=60\\ x^2+x-42=0\\ (x-6)(x+7)=0\\ \text{x has to be positive so it is 6}$$

Number that are british is x+2x+8 = 3x+8 = 18+8 = 26

$$P(british)=\dfrac{26}{60}=\dfrac{13}{30}$$

EDIT:    Sorry this is not  right

I overlooked the fact that the painting must be from the 20th century (T) to start with.

There are 30 in from the 20th century

6 of those are british

P( that it is british given that it IS from the 20th century) = 6/30 = 0.2

Melody  Apr 21, 2018
edited by Melody  Apr 21, 2018