I know that a block usually takes 10 minutes on average to get confirmed. But what is the probability that this will happen?

I mean is there any formula that we can use to calculate the probability that a block will be confirmed in the bitcoin network within x minutes? (assuming that the resources are fixed in the whole network)

The time T until a block is mined follows an exponential distribution. Assuming the difficulty has properly calibrated to the network hash rate, the rate parameter for T will be λ = 1/10 per minute. So the probability that the block is mined within t minutes is P(T <= t) = 1 - exp(-t/10).

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