# Probability Range Question

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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If this is homework, please add the homework tag. Drawing a Venn diagram (or, preferably, a Karnaugh map) will help you puzzle out the answer. For example, $$P(A) + P(B) > 1 \Rightarrow P(A\cap B) > P(A) + P(B) - 1$$ will give you a bound. –  Dilip Sarwate Mar 7 '12 at 13:50
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