Question 374877
If you have numbers from 1 to 999 in a bag and you pull out 10 numbers, what are the odds that 7 of those numbers will be from 700 to 999? Is there a formula for figuring this out and if there is can you send it to me? Thanks for your help. Pam


999 numbers
700 to 999 is 300 numbers
P(r) =  C(n,r) * p^r * q^(n-r)
q = 1 - p
C(n,r) = n!/(r! * (n-r)!)
r successes in n tries
C(10,7) = 10!/(7! * (10 - 7)!)
C(10,7) = 10!/(7! * 3!)
C(10,7) = (8 * 9 * 10)/(1 * 2 * 3)
C(10,7) = 720/6 = 120
p^r = (300/999)^7
q^(n - r) = (699/999)^3
P(7) = 120 * (300/999)^7 * (699/999)^3
0.00905329504280360257128551493191386
P(7) = 0.009053 rounded to 6 places
P(7) = 0.9053 %