How can i find the following probabilities? Let $X$  be binomially distributed with $n = 60$ and $p = 0.4$. Now i have to compute
(a)$P(20\leq X$ or $X\geq40)$ 
(b)$P(20\leq X$ and $X\geq10)$ 
i know $P(x\leq X)=\sum_{k=x}^{60}\binom{60}{k}(0.4)^k(0.6)^{60-k}$ 
But i don't know how to compute the probability when it includes or and.
How can i compute (a) and (b)?
 A: (a) This is true precisely if $X\ge 20$.
(b) This is true precisely if $X\ge 20$.
So you got a two for one deal!
For (a), the condition $X\ge 40$ is automatically fulfilled if $X\ge 20$. So if you will be happy if $X\ge 20$ or $X\ge 40$, you will be happy precisely if $X\ge 20$.
For (b),  if you will be happy if both conditions hold, your condition for happiness is $X\ge 20$.  
Remark: Please note that if the inequality signs were not indicated correctly, the analysis changes.
I do not know whether you are expected to use software to find the required sum "exactly," or whether you are expected to use the normal approximation to the binomial. 
A: Hints:
(a) Draw a number line of possible values for $x$. What do you see?
More hints:

 
 Note that we see that the stated condition is the same as finding $P(X \ge 20)$. Simply plug into the formula.

(b) Draw another number line. Note that this time it says "and", so you have to find where both (not one) of the conditions are satisfied.
More hints:

 Drawing the number line, we see that the conditions are both true whenever $X \ge 20$, so we just find that probability.

