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.

Question

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.)

Answer 1

The probability of not matching any lucky numbers out of 20 is $\frac{60}{80} \times \frac{59}{79} \times \frac{58}{78} \times \cdots \times \frac{42}{62}$. Therefore, the probability of matching at least 1 lucky number is $1-$ (probability of not matching any lucky numbers) = $1-\left(\frac{60}{80} \times \frac{59}{79} \times \frac{58}{78} \times \cdots \times \frac{42}{62}\right) \approx \boxed{95.9\%}$.