SOLUTION: 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,

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.
----------------------
If she does not have red hair, the probability of her having freckles is 1/16 .
P(f |not red) = 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.
P(f) = P(f |red) + P(f |not red) = (3/4) + 1/16 = 13/16
--------------------------------------------------------------
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
--------------------
Cheers,
Stan H.
--------------
RELATED QUESTIONS
Suppose the probability that a person has red hair is .15. If 7 people are selected at... (answered by htmentor)

The information in the following table refers to hair and eye color. If a person is... (answered by ikleyn)

The probability that the children of a certain couple will have red hair is 0.223. If the (answered by jim_thompson5910)

the probability of randomly drawing a person with red hair is 12%. if you randomly draw 3 (answered by stanbon)

Of the last 60 people that came to the cash register in a department store, 12 had blonde (answered by Fombitz)

According to a recent survey, 50% of people have brown hair, 25% of people have blonde... (answered by math_tutor2020,ikleyn)

of the last 60 people who went to the cash register at a department store, 10 had blonde... (answered by stanbon)

Of the last 60 people who went to the cash register at a department store,10 had... (answered by ikleyn)

60 people went to a cash resister at a deperatment store. 10 had blonde hair, 17 had... (answered by rfer)

. A particular hair treatment program has caused hair growth in 70% of its users. A... (answered by edjones)

SOLUTION: 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,

SOLUTION: 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,