Question

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.

(a) If a woman is chosen at random from the population, what is the probability that she will have freckles? Hint: women may have freckles regardless of the color of their hair.

Answer?

%

(b) If a woman will have freckles, what is the probability that she has red hair?

Answer?

%

Answer 1

Make a tree-diagram, two main brances as R and NR , (red and non-red)
each of those has sub-brances of F and NF
place the probabilities on each branch

you have 4 possible outcomes
R-F = (1/4)(3/4) = 3/16
R-NR = (1/4)(1/4) = 1/16
NR-F = (3/4)(1/16) = 3/64
NR-NF = (3/4)(15/16) = 45/64

And there you have it! , just convert to percentages,
notice the 4 outcomes add up to 1