The author asserted that the probability of the event in question was approximately

(1 - 10^-21)¹⁰²⁵

How small is this number?

My solution gives me something rather close to 1, but since everyone else gets something close to 0 i'm probably doing something wrong.

Here is my calculation anyway:

First I work out the value inside the brackets (1 - 10^-21)

10^-21 is a very small number 0,000000000000000000001 (21 zeros and a 1)

1 - 10^-21 is very close to 1 then: 0,999999999999999999999, I'll call this value a from now to save me writing out all those 9's.

a^10^25 is the same as a^250, with a being nearly 1 taking it to the power of 250 only makes it slightly smaller

The final answer i get is 0,99999999999999999975, which is pretty close to 1.