user134507: I know that block interval in bitcoin blockchain is exponential distribution. Now I want to know what is the probability that maximum of 3 block will be mined in the next 20 minute?

user208: Assuming block finding is a Poisson process with rate 1 per 10 minutes.
In that case, the number of blocks found per given finite time interval would be described by a Poisson distribution. For 20 minutes, a Poisson distribution with lambda = 20 minutes / 10 minutes = 2.

No blocks in 20 minutes: ~13.53%
1 block in 20 minutes: ~27.07%
2 blocks in 20 minutes: ~27.07%
3 blocks in 20 minutes: ~18.04%
4 or more blocks in 20 minutes: ~14.29%

Due the memorylessness of the Poisson process, it doesn't matter when you start the clock for your 20 minutes. These hold for whatever window of 20 minutes you look at.

134507: <p>I know that block interval in bitcoin blockchain is exponential distribution. Now I want to know what is the probability that maximum of 3 block will be mined in the next 20 minute?</p>
 208: <p>Assuming block finding is a Poisson process with rate 1 per 10 minutes.</p>
<p>In that case, the number of blocks found per given finite time interval would be described by a Poisson distribution. For 20 minutes, a Poisson distribution with lambda = 20 minutes / 10 minutes = 2.</p>
<ul>
<li>No blocks in 20 minutes: ~13.53%</li>
<li>1 block in 20 minutes: ~27.07%</li>
<li>2 blocks in 20 minutes: ~27.07%</li>
<li>3 blocks in 20 minutes: ~18.04%</li>
<li>4 or more blocks in 20 minutes: ~14.29%</li>
</ul>
<p>Due the memorylessness of the Poisson process, it doesn't matter when you start the clock for your 20 minutes. These hold for whatever window of 20 minutes you look at.</p>
