4-digit random draw, probability of getting the same number.
I can help you calculate the probability of getting the same 4-digit number on the first and second draw, as well as the probability of not getting the same number from the third to the tenth draw.
1. Probability of getting the same number on the first and second draw:
The total number of 4-digit numbers between 1001 and 9999 is 9000 (9999 – 1001 + 1).
To calculate the probability of getting the same number on the first and second draw, we can break it down into two steps:
– Probability of picking any specific 4-digit number on the first draw: 1/9000
– Probability of picking the same number on the second draw: 1/9000
So, the overall probability of getting the same number on the first and second draw is (1/9000) * (1/9000) = 1/81,000,000.
2. Probability of not getting the same number from the third to the tenth draw:
After the first and second draws, we have 8 more draws left (for a total of 10 draws). Since we already know that we can’t get the same number on the first two draws (with probability 1 – 1/81,000,000), we have 8,999,999 numbers left that we can pick on each of the remaining draws.
The probability of not getting the same number on each of the remaining draws is (8,999,999/9,000,000), because we have 8,999,999 favorable outcomes (picking a different number) out of 9,000,000 possible outcomes (all 4-digit numbers except the one picked on the first and second draw).
So, the probability of not getting the same number from the third to the tenth draw is (8,999,999/9,000,000)^8, since there are 8 draws left. Calculate this value to find the overall probability.
Let’s calculate this:
(8,999,999/9,000,000)^8 ≈ 0.9999998889
So, the probability of not getting the same number from the third to the tenth draw is approximately 0.9999998889, which is very close to 1. This means that it’s highly likely that you won’t get the same number on any of the remaining draws after the first two.
Thank you for reading my post, I hope you read other posts.
