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

Answer:

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

Step-by-step 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-$\frac{20}{80}$ or 1-0.25, which is $\frac{60}{80}$ 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 $0.75^7$