Question

Data Management: A jury of 12 people is to be chosen randomly from a list containing 10 men and 12 women. What is the probability that there is a least one man on the jury?

Answer 1

would be easier to find the probability of getting no men on the jury, then taking 1 - that probability

so getting all women, we have 12 women out of a possible 22 people so

P(only women) = (12/22)(11/21)(10/20)(9/19)(8/18)(7/17)(6/16)(5/15)(4/14)(3/13)(2/12)(1/11)

then P(at least one man) = 1 - P(only women)

Answer 2

so i would divide all those in the brackets then times them to find my answer?

Answer 3

Limited statistics memory, but I believe you multiply first before dividing...?

Answer 4

yeah it's just a series of fractions so you'd multiply across all the numerators to get 12 factorial, then 22 * 21 * 20... *11 for the denominator, then divide first quantity/second quantity

Answer 5

i'm sure there's an easier way to express this w/ factorial notation, it's just slipping my mind at the moment

Answer 6

oh ok thanks guys ill try it out and see if get it!!

Answer 7

for large calculations I would just chuck it into wolframalpha.com and let it simplify the fraction

Answer 8

or symbolab.com

Answer 9

oh ok, never heard of these sites thanks ill use them rn to make it easier, again thanks guys!!<3

Answer 10

♥

Answer 11

hey uh for the part when you said "yeah it's just a series of fractions so you'd multiply across all the numerators to get 12 factorial, then 22 * 21 * 20... *11 for the denominator, then divide first quantity/second quantity" i understand the numerator part but can you explain the denominator part a bit more?

Answer 12

like, if you have

(A/B) * (C/D) you'd multiply the numerators (A*C) and then the denominators (B*D), then the final result is (A*C)/(B*D)

same logic with (12/22)(11/21)(10/20)(9/19)(8/18)(7/17)(6/16)(5/15)(4/14)(3/13)(2/12)(1/11)

for the numerators multiply 12 * 11 * 10... etc.

for the denominators multiply 22 * 21 * 20 * 19 * 18... * 11

Answer 13

i got 3.0974447e+14 idek what the e is lol please help

Answer 14

that seems like \[3.0974447\times10^{-14}\]

Answer 15

e is an exponent

setting my calculator in fraction mode gives me 646645/646646 as the sol'n

Answer 16

You can use "e(numerical value)" instead of "\(10^{\text{numerical value}}\)"

Answer 17

Sorry, that should be \(10^{14}\) not negative 14. My bad

Answer 18

so when it comes down to what the fraction should be would it be " 12!/3.0974447e14 " ??

Answer 19

product is written as

1 - (12/22)(11/21)(10/20)(9/19)(8/18)(7/17)(6/16)(5/15)(4/14)(3/13)(2/12)(1/11)

which can be written as

1 - (12!)/(22*21*20*19*18*17*16*15*14*13*12*11) which simplifies into 646645/646646

Answer 20

so 1-1? 0 is the answer?

Answer 21

@Vocaloid

Answer 22

"1 - (12!)/(22*21*20*19*18*17*16*15*14*13*12*11) which simplifies into 646645/646646"

indicating that 646645/646646 is the solution.

Answer 23

sorry i keep asking repetitive questions but i know you said that is the solution but i gotta find the probabilty as in a percentage or fraction so when i divided those two numbers i got 99%.. is that what my answer should be or am i way off?

Answer 24

"percentage or fraction" seems to imply that 646645/646646 would be an acceptable solution

however, if you must report the solution as a percentage, then yes, 99% would be an acceptable solution

do they specify how many digits to round to?

Answer 25

no they dont the question i posted above which was "A jury of 12 people is to be chosen randomly from a list containing 10 men and 12 women. What is the probability that there is a least one man on the jury?" was all they asked

Answer 26

hm. 646645/646646 is more accurate, 99% could work too

Answer 27

alright thanks so much for the help i really appreciate it!!