How to interpret this information in probability?

Question

Given a sentence "in a jar full of marbles, 10 percent of black marbles are plastic"

Suppose $A$ is the event of being a black marble and $B$ the event of being plastic. How should I interpret this information? There are two ways I could think to interpret the information, first the probability of both being a black marble and a plastic marble is $10/100$. The other way I could interpret it is the probability of a ball being plastic given it's a black ball is $10/100$ I can't tell which one is appropriate.

Is it $$ \mathbb{P}(A \cap B)=\frac{10}{100} \quad \text{or} \quad \mathbb{P}(B |A)=\frac{10}{100}?$$

Answer 1

(b) Suppose there are 100 black marbles in the jar. Then 10 of those black marbles are plastic.

(a) Would suppose there are 100 marbles in the jar and that 10 of them are both black and plastic. How many more are black and glass (granite, lava, marble, or whatever) is not disclosed.

Answer 2

As you can see, from the table, the right answer is the second option, a conditional probability,

$$\mathbb{P}(B \vert A)=\frac{10}{100},$$

i.e.

$$\mathbb{P}(\text{plastic}\,\vert\, \text{black})=\frac{10}{100}.$$

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The more detail answer:

From the assignment

In a jar full of marbles, $10$ percent of black marbles are plastic.

we know nothing about the second row (“No black”), we are restricted (= conditional probability) by the black marbles only (“… $10$ percent of black marbles …”).

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Note:

There is no possibility to calculate $\mathbb{P}(A \cap B)$ not knowing anything about total number of marbles (black and non-black) in a jar.