In a certain town 45% of the people have black hair,30% have brown eyes and 20% have both black hair and brown eyes.if a person is selected at random from the town,

What is the probability that he has brown eyes and doesn't have black hair?

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- May 29th 2009, 09:14 PMchange_for_betterHow can i solve this probability question?
In a certain town 45% of the people have black hair,30% have brown eyes and 20% have both black hair and brown eyes.if a person is selected at random from the town,

What is the probability that he has brown eyes and doesn't have black hair? - May 29th 2009, 11:12 PMmatheagle
Let A=black hair, B=brown eyes.

P(A)=.45, P(B)=.3 and P(AB)=.2.

You want , where the prime denotes the complement.

I would use .

SO , GIVING YOU .

My question is where is the probability that this person is male? - May 29th 2009, 11:25 PMchange_for_better
- May 29th 2009, 11:34 PMmatheagle
- May 29th 2009, 11:39 PMchange_for_better
- May 29th 2009, 11:41 PMmatheagle
why?

20% have both black hair and brown eyes

means, to me, P(AB)=.2.

I left out the basic subtraction earlier today.

I expected you to finish, but I am tired and I just went back and finished the problem for you.

All I wanted, was for you to subtract .2 from .3. - May 29th 2009, 11:50 PMchange_for_better
- May 29th 2009, 11:54 PMchange_for_better
- May 30th 2009, 07:45 PMmatheagle
- May 31st 2009, 01:57 AMHallsofIvy
Here's how I would do that problem. Imagine the town has 1000 residents. Then 30% of 1000= 300 people have brown eyes and 20% of 1000= 200 people have both brown eys and black hair. That leaves 300- 200= 100 who have brown eyes but NOT black hair. The probability of selecting such a person, all people in town being equally likely, is 100/1000= .10.

And, as matheagle pointed out, .3/.45 is NOT .6! - May 31st 2009, 05:01 AMmr fantastic
Well, if we're showing different approaches then here's mine.

Make a Karnaugh table (since I'm hopeless with formulas):

Now it's like a simple Sudoko puzzle to fill in the rest of the probabilities:

I'm sure you can fill in the last square.

So the answer to the question "What is the probability that [the person] has brown eyes and doesn't have black hair?" is easily read from this table to be 0.1.

**However**, since no information is given about males and females, the actual question "What is the probability that he has brown eyes and doesn't have black hair?" cannot be answered.