A shop has only red, green and blue carpets. $60 %$ of the carpets have red colour, $30 %$ have green colour and $50 %$ have blue colour. If no carpet has all the three colours, what percentage of the carpets have only one colour?

35 %

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40 %

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50 %

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60 %

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Solution

The correct option is D $60 %$
60% of carpets have red colour
P(only R)+P(R $\cap$ G) +P(R $\cap$ B)=0.6
P(only B)+P(B $\cap$ G) +P(B $\cap$ R)=0.5
P(only G)+P(G $\cap$ B) +P(G $\cap$ R)=0.3
On adding we get,
P(only R)+P(R $\cap$ G) +P(R $\cap$ B)+P(only B)+P(B $\cap$ G) +P(B $\cap$ R)+P(only G)+P(G $\cap$ B) +P(G $\cap$ R)=1.4
Also,P(only R)+P(only B)+P(only G)+P(R $\cap$ G) +P(R $\cap$ B)+P(G $\cap$ B) =1
On solving we get
+P(R $\cap$ G) +P(R $\cap$ B)+P(G $\cap$ B) =04
,P(only R)+P(only B)+P(only G)=0.6
Therefore percentage of carpet having only one colour=60%

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