It is about 33% vs 100%
That implies there is complete certainty that a block will be mined within the next 10 minutes, which is false. The probability that at least one block is found within the next 10 minutes is not 100%, but 63.2%. Explanation in here.The probability that k blocks are mined within the next t minutes is: P(X = k) = e^(-λt) * (λt)^k / k!
For k=3, the probability that at least 3 blocks are mined within the next t minutes would be P(X >= 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2).
Applying with λ = 0.1 (blocks per minute), t = 3 minutes, X = 0, 1, 2 blocks, and you have:
- P(X = 0) = 2.718^(-0.3) * (0.3)^0 / 0! = 0.7408
- P(X = 1) = 2.718^(-0.3) * (0.3)^1 / 1! = 0.2222
- P(X = 2) = 2.718^(-0.3) * (0.3)^2 / 2! = 0.0333
=> P(X >= 3) = 1 - 0.7408 - 0.2222 - 0.0333 = 0.0037.
So, the probability that at least 3 blocks are mined within the next 3 minutes is 0.37%. Pretty rare.
