Factory has 125 employees. 20% of employees are women. 32% of the women smoke and 40% of the men smoke.?

Question

If 3 people are chosen at random, what's the probability that they are all either smokers or women? (This problem deals with probability and statistics).

Answer 1

I believe it goes something like this---

20% of workers are women, therefore, 25 women.

32% of those are smokers, therefore, 8 women smokers.

80% men, therefore, 100 men.

40% smoke, therefore 40 male smokers.

chance of choosing a woman is 25 of 125 = 1 in 5.

chance of choosing a smoker is 48 of 125 = 1 in 2.6

chance of choosing 3 ALL WOMEN would be 1 in 5  - -- times 3, or about 1 in 15.

chance of choosing 3 ALL SMOKERS would be 1 in 2.6 - - -times 3, or about 1 in 8.

But this is a more simplified form. Actually, as you choose each person, the chances change slightly, for example, after you chose the first person, perhaps a woman, the chance of choosing another woman is not really 1 in 5 anymore, since that first woman is now out of the pool, and the chance of choosing another woman changes to 24 out of 124 people,  or about 1 in 5.16, so each choice slightly changes the following choice if you are pulling people out of the pool... this might be too complicated, and the 1 in 15 chance might be enough for your answer.

Answer 2

20% of 125 is 25 so there are 25 women and 100 men.  $0% of 100 is 40 so 40 men smoke.  So the number of smokers or women is 25 + 40 = 65. The 32% women that smoke is a "distractor" and has no effect on the solution to the problem, as you don't care if the women smoke, it just asked for women.

So to pick three that are all either women or smokers, it's

65/125 X 64/124 X 63/123 since each time you pick one there is one less to pick the next time.  So either write that, or do it out.