In a simplified game of \"Keno\", players choose distinct numbers from 1 through
ID: 3203584 • Letter: I
Question
In a simplified game of "Keno", players choose distinct numbers from 1 through 80 on a scantron like card. Often, players may choose how many numbers to bubble in (up to 5). Five numbers are chosen at random (with equally likely outcomes). Players win based off of how many numbers match between their number choices and those drawn.
a) Assuming a player chooses five numbers, what is the probability that all five of their choices are drawn?
b) Assuming a player chooses four numbers, what is the probability that all four of their choices are drawn?
Explanation / Answer
(a)
Total number of ways of selecting 5 numbers out of 80 is
C(80,5) = 24040016
Since all the 5 numbers can be matched in only one way so the probability that all five of their choices are drawn is
1/ 24040016 = 0.0000000416
(b)
Number of ways of choosen 4 numbers out of 5 drawn numbers is C(5,4) = 5
So the probability that all four of their choices are drawn is
5/ 24040016 = 0.000000208