The probability that a blue eyed person is left handed is 1/7. The probability that left handed person is blue eyed is 1/3. The probability that a person has neither of these attributes is 4/5. What is the probability that a person has both these attributes?

Question

anonymous · Answer

1/21

anonymous · Answer

the answer is 1/45 though

anonymous · Answer

woah! how? i thought you just multiply the demoninators...

anonymous · Answer

im sorry.. :(

anonymous · Answer

somewhere i must use conditional probability but what is given in P(L|B)

anonymous · Answer

ohh, never used conditional probability..

anonymous · Answer

its ok :) like, is the question saying that, given the person is blue eyed...the prob that the person is left handed is 1/7?

anonymous · Answer

just re-reading, how does that make sense? their both blue eyed and left handed..

anonymous · Answer

i am very confused...

phi · Answer

The probability that a blue eyed person is left handed is 1/7
For example, we can assign 6 blue eyed to "only blue eyed" and 1 in the intersection with left handed.  
The probability that left handed person is blue eyed is 1/3.  We could, for example, assign 2 people to only left-handed and 1 to both blue eyed and left-handed
There are a total of 9 people in these categories
Probability of neither of these attributes is 4/5.  So these 9 people represent 1/5 of the total population, which must be 5*9= 45.   4/5 or 36 of the population are outside the 2 circles.

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Looking at the picture, we see only 1 out of 45 fits the category both blue eyed and left-handed.