# Probability of choosing 4 person

1. Jul 25, 2014

### desmond iking

1. The problem statement, all variables and given/known data

for part b , my working is (12c2 x 18c2)/(35c4) = 0.192

thers're 12 women doctor , 2 are chosen , there're 18 male left, 2 are chosen . no condition= choose 4 person from 35 person.

but the ans is 0.807

2. Relevant equations

3. The attempt at a solution

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2. Jul 25, 2014

### Orodruin

Staff Emeritus
In the case of b the men have nothing to do with it. You already know that two women were selected and you must condition your probability to this, i.e., given two women from the attendees - what is the probability that both are doctors?

3. Jul 25, 2014

### D H

Staff Emeritus

You computed the probability that a randomly selected panel will have two female doctors. That is not the question. Some of those randomly selected panels will have zero females, others one, others three, yet others four. You need to exclude all of these because it's a given that two of the panel members are female.

I don't know what the answer sheet calculated, but it too is wrong.

4. Jul 27, 2014

### desmond iking

why the men have nothing to do with the 2 women doctor chosen? the question want 4 members in the panel. am i right? if so, my working is 12x11 /(17x16)=0.49

since we already know there're 17 women , after 1 is chosen 16 left. there're 12 woman doctor, after 1 is chosen, 11 left. am i correct?

5. Jul 27, 2014

### HallsofIvy

Staff Emeritus
Part b says "given that two women are selected what is the probability that both are doctors". That is exactly the same as if the problem had said "if there are two women chosen from 17, 12 of whom are doctors, what is the probability both women chosen are doctors?" without mentioning men at all. Yes, that is $\left(\frac{12}{17}\right)\left(\frac{11}{16}\right)$.

6. Jul 27, 2014

### desmond iking

for part a , can i do in this way? P(DDDE) + P(EDDD) + P(DEDD) +P(DDED) =
( (20/35) x (19/34) x (18/35) x (15/32) ) x 4 = 0.327

the correct working would be (20C3 X15C1)/35C4 = 0.327

Is my concept wrong? D=doctor E=engineer

why by using the method of C (combinations) , the arrangment of person is not importamt , which means i dont need to times 4 compared to the method i used above

7. Jul 30, 2014

### desmond iking

8. Jul 30, 2014

### Orodruin

Staff Emeritus
You can do it in either of the ways. In the first way, you are taking the probability of choosing a particular ordered set and there are 4 such ordered sets that give you the sought result.

When you study the number of combinations you are studying the number of unordered sets both in denominator and numerator.

9. Jul 30, 2014

### haruspex

I suspect part (b) is intended to be interpreted in the context of part (a), i.e., given 3 doctors are selected and two women are selected. This gives an answer much closer to the book one, but I still don't get .807 (which is very close to 46/57). I get 22/29.

10. Jul 30, 2014

### D H

Staff Emeritus
Hmm. That's a possibility. I get 38/45 with that interpretation. (Again, not 0.807.)