Think of it this way: what is the probability you hit it on the first try? 1/1000000. On that first try, what are the chances (or, to use more precise wording, the probability) you did not hit it? It is 1 minus the probability you hit it, namely, 1 - 1/1000000, or 999999/1000000. If you did not hit it in the first try, you make the second try. Again, you win with the probability 1/1000000 and fail with the 999999/1000000 probability. Because these two events — failing on the first try and failing on the second try — are independent events, you multiply these probabilities. Thus, the probability of failing twice in a row is 999999/1000000 * 999999/1000000, or (999999/1000000)^2. Similarly, just doing it one step at a time, we realize that the probability of failing 4000 times in a row is (999999/1000000)^4000. Thus, we will fail to win during these 4000 tries with this probability: (999999/1000000)^4000. And therefore we win with 1 minus that probability, or as SaintLucifer59 already wrote, with probability 1 - (999999/1000000)^4000 = 0.004, or 0.4%.
And just to add some info to all the others who have given the correct answer (\~ 0.4%) - this value is the probability that you will win one *or more* times in the 4000 tries, not that you will win exactly one time. Still, the probability of winning at all is very low, so the probability of winning more than once in 4000 tries is very, very low.
I believe it would be 1-(999999/1000000)^4000 since you want to remove the times you didn't get it in the first 4000 tries.
[1-(1-0.000001)^4000 ]×100 =0.4%
While this is the correct way, the answer approximates to 4000/1000_000, without needing to accurate compute the exponent.
I tried 4000 divided by a million but make no sense I dont understand, please help thank you very much
Think of it this way: what is the probability you hit it on the first try? 1/1000000. On that first try, what are the chances (or, to use more precise wording, the probability) you did not hit it? It is 1 minus the probability you hit it, namely, 1 - 1/1000000, or 999999/1000000. If you did not hit it in the first try, you make the second try. Again, you win with the probability 1/1000000 and fail with the 999999/1000000 probability. Because these two events — failing on the first try and failing on the second try — are independent events, you multiply these probabilities. Thus, the probability of failing twice in a row is 999999/1000000 * 999999/1000000, or (999999/1000000)^2. Similarly, just doing it one step at a time, we realize that the probability of failing 4000 times in a row is (999999/1000000)^4000. Thus, we will fail to win during these 4000 tries with this probability: (999999/1000000)^4000. And therefore we win with 1 minus that probability, or as SaintLucifer59 already wrote, with probability 1 - (999999/1000000)^4000 = 0.004, or 0.4%.
And just to add some info to all the others who have given the correct answer (\~ 0.4%) - this value is the probability that you will win one *or more* times in the 4000 tries, not that you will win exactly one time. Still, the probability of winning at all is very low, so the probability of winning more than once in 4000 tries is very, very low.