# probability help

#### ecohelp

##### New Member
I'm not looking for simply the answer but i need to know the step by step solution process, and what formula you used if any to solve for it please. Any help will be appreciated.

70% of the people applying for a job are accepted. What is the probability that among the next 18 applicants exactly 10 will be accepted?

#### quark

Welcome ecohelp.

This is a binomial probability with n=18, p=0.70

When the number of events X=10, we have:

P(X=10) = (18 choose 10) * 0.7^10 * (1-0.7)^8 = 0.0811

Hope this helps.

#### ecohelp

##### New Member
Thanks. I located the binomial probability distrubution formula, and came up with the same answer =)

I attempted to use the formula with this question but I'm not getting the correct solution? Same problem but asking for the following:

70% of the people applying for a job are accepted. What is the probability that among the next 18 applicants, exactly 5 will be rejected?

The answer is: .2017, but I don't know how it is found?

Here is what I started doing p=.7, n=18, x=5

I plugged it into f(x)=n!/x!(n-x)! * p^x (1-p)^(n-x)

=18!/5!(18-5)!*7^5 (1-.7)^(18-5)

=1028160/120*16807*(.3)^13

=22.95862001????? what am I doing wrong? I'm really confused I did this 5x and still the same answer....

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2nd problem how do you solve when the question is stated like this:

70% of the people applying for a job are accepted. What is the probability that among the next 18 applicants, fifteen or more will be accepted?

Can you tell me how they got that answer because again I am getting a totally different outcome.....

#### ecohelp

##### New Member
okay I figured out what i was doing wrong on the problem with "exactly 5 will be rejected" i should have put x=13 (because 18-5rejected), and finally I got the correct answer .2017

But, I still need help on the last problem how do you solve when they ask for fifteen or more will be accepted??? I don't know how to get the answer .1646?

#### quark

Since n=18, P(X=15 or more) = P(X=15)+P(X=16)+P(X=17)+P(X=18)
and apply the binomial formula.

#### ecohelp

##### New Member
so i have to 1st solve for x=15 and plug it into the binomial formula, then work it out again for x=16, and again for x=17, and once more for x=18

then finally add the solutions for all 4 answers, and come up with a total?

#### ecohelp

##### New Member
okay nevermind, I got it

p=.7
n=18
x=15, 16, 17, 18
then add up the solution for each one and get 1 final total answer

after all the calculations I ended up getting
x=15: .104598275
x=16: .045761746
x=17: .0125620475
x=18: .0016284136

therefore .104598275+.045761746+.0125620475+.0016284136=.1645504821 which rounded is basically .1646

thanks you quark for the quick response, and your help =) much appreciated!