Question
Imagine a keno game where the numbers are drawn WITH replacement. In other words, 20 balls are drawn from an urn with balls numbered 1 to 80, one at time. As each ball is drawn the number is noted, and then the ball is returned to the urn. The player picks four different numbers from 1 to 80. For each number picked it is considered a match if the casino draws that number at least once. What is the probability for each possible outcome of 0 to 4 matches?
Answer
| Problem 205 Answer | ||
| Matches | Probability | |
| 4 | 0.001906 | |
| 3 | 0.031326 | |
| 2 | 0.179819 | |
| 1 | 0.428464 | |
| 0 | 0.358486 | |
| Total | 1 | |
Acknowledgement: My thanks to Eliot J. for this help with this problem.
Michael Shackleford, ASA — June 2, 2009