If a jury list contains 20 men and 20 women, what is the probability of randomly selecting 12 members that are all men?

Question

caution0 · Answer

50/50 
is this a bubble in question??

dunnitagainn · Answer

if you mean multiple choice no, it is free response?

dunnitagainn · Answer

would it be 50/50 for all 12 people?

caution0 · Answer

cant really tell you the answer straight out.. im trying to figure out a way to explain it

caution0 · Answer

2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.

zarkon · Answer

have you done permutations/combinations

dunnitagainn · Answer

why does there have to be at least 2/3 of the jury as men?

caution0 · Answer

455 ways to select a jury of 12 from a pool of 15
 1 way to select all 5 women
120 ways to select 7 men from a pool of 10
 120 ways to select a jury with fewer than 8 men

caution0 · Answer

(455-120)/455 = 335/455 = 67/91

caution0 · Answer

does that help??

dunnitagainn · Answer

yeah it does thank you

caution0 · Answer

no problem ^.^

zarkon · Answer

really?  that is not even close to the answer

caution0 · Answer

how ???

zarkon · Answer

why are you talking about 5 and 7 and 8


this is a simple hypergeometric distribution problem

dunnitagainn · Answer

that was confusing me, i thought i must be doing it wrong

zarkon · Answer

out of the 20 men choose 12

out of the 40 people choose 12

then divide

dunnitagainn · Answer

so (12/20) * (12/40) ?

zarkon · Answer

$$\frac{_{20}C_{12}}{_{40}C_{12}}$$

caution0 · Answer

well ig i was doin it wrong.. looks like he got it

zarkon · Answer

the probability will be a very small number

dunnitagainn · Answer

Im not sure what the c is? we have not learned that

zarkon · Answer

ok


look at the number of choices you have ...

when choosing the men you have 20 choices for the 1st guy, 19 for the sec....as so on..

this gives $$20\times 19\times\cdots\times 9$$ number of ways the pick the guys

zarkon · Answer

then the number of ways to pick 12 people from 12 is 

$$40\times 39\times\cdots\times 29$$

zarkon · Answer

then divide

$$\frac{20\times 19\times\cdots\times 9}{40\times 39\times\cdots\times 29}$$

dunnitagainn · Answer

okay, thats what i did earlier, but i thought i was doing it wrong because it was so many steps, thank you so much!!!

zarkon · Answer

np