Question

help! Can some explain why P(X≥1)=1-P(X=0)

Answer 1

if that's true, you mean that:

\(P(X≥1)=1-P(X=0)\)

And that
\(1= - P(X≥1)- P(X=0)\)

None of which makes sense :((

Answer 2

Looks like \(X\) is a random variable with a discrete distribution. If it's a proper distribution, then \(\sum\limits_x\mathbb P(X=x)=1\).

The support appears to be non-negative integers, so the sum translates to
\[\sum_{x=0}^\infty\mathbb P(X=x)=1\iff \mathbb P(X\ge0)=1\]
We could take one term out of the sum, then we have
\[\mathbb P(X=0)+\sum_{x=1}^\infty\mathbb P(X=x)=1\iff \mathbb P(X\ge1)=1-\mathbb P(X=0)\]