We looked at the popular casino game keno, in which a player chooses numbers from 1 to 80 and hopes that the casino will draw balls with the same numbers.
A player can choose only 1 number or as many as 20. The casino will then pick 20 numbered balls from the 80 possible; if enough of the player's numbers match the lucky numbers the casino chooses, the player wins money. The amount won varies according to how many numbers were chosen and how many match.
Watch the video below then answer the question.
Keno Revisited
If 20 numbers are chosen, find the probability of matching at least 1 lucky number. (Round your answer to one decimal place.)
The probability of not matching any lucky numbers is:
(60/80) x (59/79) x (58/78) x ... x (41/61)
This is because there are 60 numbers that are not chosen out of 80 on the first draw, 59 numbers that are not chosen out of 79 on the second draw, and so on, until there are 41 numbers that are not chosen out of the remaining 61 on the last draw.
So, the probability of matching at least 1 lucky number is:
1 - (60/80) x (59/79) x (58/78) x ... x (41/61)
Using a calculator, this simplifies to approximately 0.9707.
Therefore, the probability of matching at least 1 lucky number when 20 numbers are chosen is approximately 0.9707, or 97.1% (rounded to one decimal place).