# Math Help - Find P(smoking woman)

1. ## Find P(smoking woman)

A city has 40% men and 60% women, 50% of the men are smoking, 30% of women are smoking. Find P(smoking woman).

2. ## Re: Find P(smoking woman)

Originally Posted by razemsoft21
A city has 40% men and 60% women, 50% of the men are smoking, 30% of women are smoking. Find P(smoking woman).
Have you considered drawing a tree diagram? It should make the 1-step calculation very obvious.

P(woman)=0.6

P(if woman, smokes)=0.3

Assume there are 100 people. Then, there are 40 men and 60 women. 30% of these 60 women smoke, out of the total 100. A quick calculation leads to 18 out of the 100 people being female smokers.

3. ## Re: Find P(smoking woman)

Thanks, this is understood, can you use the laws of Probability please ?

4. ## Re: Find P(smoking woman)

Originally Posted by razemsoft21
Thanks, this is understood, can you use the laws of Probability please ?
$\mathcal{P}(W\cap S)=\mathcal{P}(S|W)\mathcal{P}(W)$.