New York State’s "Quick Draw" lottery moves right along. Players choose between one and ten numbers from the range 1 to 80; 20 w

Question

4 years ago

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New York State’s "Quick Draw" lottery moves right along. Players choose between one and ten numbers from the range 1 to 80; 20 w

inning 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?

Mathematics

1 answer:

Mrac [35] · Answer 1 · 2021-12-07T05:28:26+03:00

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 <em>p</em>, then the probability of an event not occurring is <em>1-p</em>. 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 $0.75^7$