KENO probability

#1
"In the game of Keno, 80 numbers are displayed on a reader board. 20 of these numbers are chosen to be the winning numbers. Suppose a person has selected 5 numbers on a playing card. What is the probability of selecting exactly 4 correct numbers?"

I really need help with this problem! I've been working at it for a while, but can't even get started correctly!!
 

JohnM

TS Contributor
#2
This is a hypergeometric probability situation:

N = size of population = 80
M = # of items in population with property "E" = 20
N-M = # of items in population without property "E" = 60
n = number of items sampled = 5
k = number of items in sample with property "E" = 4

P(k) = (M,k)*(N-M,n-k) / (N,n)

(x,y) = xCy = x! / (y!(x-y)!)


So, P(k=4) = (20,4) * (80-20,5-4) / (80,5)

= 4845 * 60 / 24040016

= 0.0121