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The probability that a hummingbird has a red beak, red eyes and a red tail are 0.7, 0.8 and 0.4 respectively. The probability that a hummingbird has all 3 and none of the three is 0.1 and 0.05 respectively.

Let $P$ be the probability that a hummingbird has a red beak, red eyes, but no red tail. What is the range of values of $P$?

I get that $P(exactly.2.of.the.3)=0.75$ but am not sure how to proceed from there.

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Use venn diagram and try manipulating the value of sets so that $P(Bleak \cap Eyes) - P(Bleak U Eyes U Tail)$ is maximum or minimum. – quartz Mar 7 '12 at 14:30

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