Question 834219
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.


<pre>
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


</pre>

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.