You have the first part right, for the second one you need to use Baye's theorem.
In a particular town 60% of the population are women. 4% of the men and 1% of the women are taller than 180 cm.
i) What % of the town's population is taller than 180 cm?
ii) If a person is chosen at random and is taller than 180 cm, what is the probability that the person is a woman?
Ummm I'm not that good at probability so could someone please give me some help?
For:
i) I did:
Percentage = 100(0.04*0.4 + 0.01*0.6)
= 0.022*100
= 2.2%
ii) I did:
P = 0.022*0.2
= 11/2500
The answers don't look rite though...
ii requires conditional probability.
Here is the magic recipe, the big secret, the great trick, the golden elixir. Read it carefully ........
Set up careful notation and definitions. Carefully define all known probabilities in terms of this notation.
Let T be the event height greater than 180 cm.
You have:
Pr(M) = 2/5, Pr(W) = 3/5,
Pr(T | M) = 1/25, Pr(T | W) = 1/100,
Pr(M and T) = Pr(T| M) Pr(M) = (1/25) (2/5) = 2/125,
Pr(W and T) = Pr(T| W) Pr(W) = (1/100) (3/5) = 3/500,
Pr(T) = Pr(M and T) + Pr(W and T) = 2/125 + 3/500 = 11/500 (= 0.022 as you found).
You require Pr(W | T).
.