Question

New York State’s "Quick Draw" lottery moves right along. Players choose between one and ten numbers from the range 1 to 80; 20 winning numbers are displayed on a screen every four minutes. If you choose just one number, your probability of winning is 20/80, or 0.25. Lester plays one number seven times as he sits in a bar. What is the probability that all seven bets lose?

Answer 1

The Answer is 0,133484. The same number as
`(60/80)^7` or
`0.75^7`

Explanation:

If the probability of an event occurring is p, then the probability of an event not occurring is 1-p. Therefore if Lester plays one number, then the probability of that number not winning is 1-
`(20)/(80)` or 1-0.25, which is
`(60)/(80)` or 0.75

`\\`Two or more events are independent if the occurrence of one does not affect the probability of occurrence of the other. In Lester's game, the probability of a number winning or not winning does not affect the probability of the same number winning or not winning in the next game.

`\\`In order to find the probability of several events occurring in succession, we multiply the probabilities of the individual events.

`\\`Therefore if Lester plays one number seven times, the probability that all seven bets lose are
`(60/80)^7` or
`0.75^7`