How do you transform probabilities from the form P[X=x] to P[X =< x]

Question

I'm working on a problem that requires you to use a binomial distribution to solve the problem.

Now we want to determine x such that

P[X > x] =< 0.01

or, equivalently,

0.99 =< P[X=<x] 

which is equal to

P[X=<x] => 0.99 (I added this part)

...

The following table summarizes the selection process for x:

x        P[X=x]                        P[X=<x]
0        (0.98)^20 = 0.668             0.668
1        20(0.02)(0.98)^19=0.272       0.940

I'm pretty sure I understand how they derived the formula for the inequality what I don't understand is how they derived the numbers that go into the table. Can somebody please explain this part? Any help would be appreciated.

Answer 1

$$ P\left(X\leq0\right) = P\left(X=0\right) = 0.668,\\ P\left(X\leq 1\right) = P\left(X=0\right) + P\left(X=1\right) $$ thus subbing your numbers in we find

$$ P\left(X\leq 1\right) = 0.668 + 0.272 = 0.94 $$