Question 1036346: In a certain population, the probability that a woman has red hair is 1/4. If a woman has red hair, the probability of her having freckles is 3/4. If she does not have red hair, the probability of her having freckles is 1/16 .
Find the following probabilities. Enter your final answers in percent notation rounded to the nearest tenth.
1)If a woman is chosen at random from the population, what is the probability that she will have freckles? My instructors hint was: women may have freckles regardless of the color of their hair.
2) If a woman will have freckles, what is the probability that she has red hair?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a certain population, the probability that a woman has red hair is 1/4.
If a woman has red hair, the probability of her having freckles is 3/4.
P(red) = 1/4
P(f | red) = 3/4 = P(red AND f)/P(red)
So, P(red AND f) = P(red)*(3/4) = (1/4)(3/4) = 3/16
Comment:: Use this for your problem #2.
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If she does not have red hair, the probability of her having freckles is 1/16 .
P(f |not red) = 1/16
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Find the following probabilities. Enter your final answers in percent notation rounded to the nearest tenth.
1)If a woman is chosen at random from the population, what is the probability that she will have freckles? My instructors hint was: women may have freckles regardless of the color of their hair.
P(f) = P(f |red) + P(f |not red) = (3/4) + 1/16 = 13/16
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2) If a woman will have freckles, what is the probability that she has red hair?
P(red | f) = P(red AND f)/P(f) = (3/16)/(13/16) = 3/13
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Cheers,
Stan H.
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