Percentage of balls that are not plastic nor gray in a jar I am trying to revive my math skills if there are any :) but I can not come up with a solution to the following problem:

You have a jar of balls. $55\%$ of the balls are gray, $45\%$ are plastic and $20\%$ are gray and plastic. What is the percentage of balls that are neither gray nor plastic?

Thank you for your help !
 A: Hint:  Look up inclusion-exclusion principle to figure out what percentage of balls are either gray or plastic.
A: $$\begin{aligned}P((\text{not }A)\text{ and }(\text{not }B))&=P(\text{not }(A\text{ or }B))\\
&=1-P(A\text{ or }B)\\
&=1-(P(A)+P(B)-P(A\text{ and }B))\end{aligned}$$
Or it's perhaps quicker to sketch a Venn diagram and completely fill out all four regions.
A: Maybe this would be a helpful way to think about it.
You have a collection of balls. If you pick a random ball then the probability that the ball is gray is $55\%$. Likewise for the other events. In fact define the events


*

*A: the ball is gray

*B: the ball is plastic


You have
$$
P(A) = 0.55 \\
P(B) = 0.45 \\
P(A\cap B) = 0.20.
$$
What you want to find is
$$
P((A\cup B)^c)) = 1 - P(A\cup B).
$$
Here the event $(A\cup B)^c$ means that neither $A$ or $B$ occur.
Take a look at this for a formula: http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle
A: For simplicity, assume there are exactly $100$ balls. You are given that $20$ are gray and plasytic. Also, $55$ are gray, so $55-20=35$ are gray and not plastic. Likewise, $45-20=25$ are plastic and not gray. The remaining $100-35-25-20=20$ are thus neither gray nor plastic.
Maybe draw a Venn diagram to support this.
