Question 834219: A new office, within an existing company, is to be established with eight occupants. Within the company there are 216 females and 258 males. Assuming an independent random selection of each office member with constant probabilities, draw up a probability distribution for the number of females in the office.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rounding to 4 decimal digits, the probability that a member of the office will be a female is .4557 and the probability that the member of the office will be a male is .5443.
it appears you are looking for a binomial distribution.
assuming that is what you are looking for, the distribution would look like this.
n x p(x) p(1-x) ncx probability of x occurrences
8 0 0.5443 0.4557 1 0.001859654
8 1 0.5443 0.4557 8 0.017769758
8 2 0.5443 0.4557 28 0.074286325
8 3 0.5443 0.4557 56 0.177459058
8 4 0.5443 0.4557 70 0.264952177
8 5 0.5443 0.4557 56 0.253172648
8 6 0.5443 0.4557 28 0.151198017
8 7 0.5443 0.4557 8 0.051598533
8 8 0.5443 0.4557 1 0.00770383
total probability >>>>> 1
n is the total number of people in the office.
x is the number of males.
p(x) is the probability that it will be a male.
p(1-x) is the probability that it will be a female.
nCx is the number of possible combinations you can get from 8 people taken x at a time..
probability of x occurrences is given by the formula:
p(x number of males is equal to: nCx * p(x)^x * p(1-x)^(n-x)
for example:
the probability there will be 5 males in the office is equal to:
8C5 * (.5443)^5 * (.4557)^3 which is equal to:
56 * (.5443)^5 * (.4557)^3 which is equal to .25317
this means there is a 25% probability that the office will contain 5 males.
i'm pretty sure this is what you want.
let me know if it's something different.
the total probability should always equal 1 which is what is shown in the table.
this is a good check to see that you did it correctly.
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