The conditional distributions describe the probability of an outcome of a random variable conditioned on the other random variable taking a particular value.

Recall that given any two events A and B, then:

$$P(A | B) = \frac{P(A \cap B)}{P(B)}$$

This result can be applied in bivariate distributions. That is, the conditional distribution of $X_1$ given $X_2$ is defined as:

$$f_{(X_1 | X_2)}(x_1 | X_2 = x_2) = \frac{f_{(X_1, X_2)}(x_1, x_2)}{f_{X_2}(x_2)}$$

So, in this case, we need:

$$f_{(X_1 | X_2)}(x_1 | X_2 = 100) = \frac{f_{(X_1, X_2)}(x_1, x_2)}{f_{X_2}(X_2 = 100)}$$

The marginal distribution of company B ($f_{X_2}(x_2)$) given by:

Company B(X₂) Profits	-50 Million	0 Million	10 Million	100 Million
P(X₂ = x₂)	0.0712	0.4228	0.3482	0.1583

Which table shows the correct conditional distribution of Company A's profits given that Company B's profits are 100 million?