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I've stumbled across a rather confusing question regarding conditional probability, and I can't seem to figure out if it contains an error or not.

The question is as follows:

Determine if the statements are examples of conditional probabilty by matching the C.

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I'm very confused. Does the question seem like it has an error (or is unfinished)? Or am I just not understanding? And how would I go about answering this question. I've attempted subtracting the various amounts (on the right) from 1, but I am unsure on what to do with this information. It does not directly correspond with P(A) or P(B). Does the question ask for P(C)? I am completely unsure whether this was worded wrong or not. Hopefully someone can give me some insight on how to understand and answer this question!

(The answers are not in order. They can be dragged around and put with their corresponding formula/probability.)

Thanks in advance!

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    "... by matching the columns." – 2017-02-20

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If $A$ and $B$ are events with nonzero probability, then the conditional probabilities \begin{align} \mathbb P(A\mid B) &= \frac{\mathbb P(A\cap B)}{\mathbb P(B)}\\ \mathbb P(B\mid A) &= \frac{\mathbb P(A\cap B)}{\mathbb P(A)} \end{align} are well-defined. Since the probability of any event is nonnegative and at most $1$, it is clear that $\mathbb P(A\mid B)\geqslant \mathbb P(A\cap B)$ and similarly $\mathbb P(B\mid A)\geqslant \mathbb P(A\cap B)$. From the given options, it follows that $\mathbb P(A\cap B)=0.30$.

Without further information, we cannot determine the quantities $\mathbb P(A\mid B)$ and $\mathbb P(B\mid A)$. This is evident by symmetry.