Understanding tables for CDF of a Binomial Distribution Disclaimer: I'm new to statistics.
Background: I'm reading Probability for Dummies by Deborah Rumsey, 2nd edition.
Quote: The author writes, "If you look at a column where p is small -p = 0.01, for example-you see more probability accumulating right away when X = 0, because the probability of success is so small; therefore, the chance of getting less than or equal to zero successes is large. The graph of the pmf is skewed to the right. And for a column where p is large-say, p = 0.99 -no probability accumulates until the later values of X, because the probability of success is large. The graph of the pmf in this case is skewed to the left."
Problem: My intuition tells me that if p is small (e.g., .01), then it's probability column should also be small, not start large (.951, .999, etc.)
Question: Does anyone have a clearer explanation of how to use this table?

 A: If $p$ is very small, $X$ will be $0$ with probability very close to $1$.  The first entry in the table, for $x=0$, is $P(X \le 0) = P(X=0)$, and that will be very close to $1$.  As you go down in the table, the numbers grow:
$$P(X \le 0) \le P(X \le 1) \le P(X \le 2) \le \ldots$$
so these will be even closer to $1$.
To get a small number in the table for $P(X \le x)$, you need $P(X>x)$ to be 
near $1$, i.e. $X$ is usually greater than $x$, and this requires $p$ to be near $1$.
A: If $p$ is small then $1-p$ is large. The cdf for $n=5$ is 
$$P(X\leq x)=\sum_{k=0}^x \binom{5}{k} p^k\cdot (1-p)^{5-k}$$
If $x=0$ then $P(X=0)=(1-p)^5$. For $p=0.01$ it becomes $P(X=0)=0.99^5=0.951$
The key point is that at the beginning of the columns $(1-p)$ is raised to power more than $p$. In the first row $n$ times. In the second row $n-1$ times...
The larger $(1-p)$ is the larger is $(1-p)^{5-k}$. This is the term which dominates the term $p^k$ at the beginning of the columns.
Since the single probabilties are summed up in case of a cdf the numbers of the columns on the left grow faster at the beginning than the numbers of the columns on the right.
