What the Clock Knows

A support team wants to predict which tickets get escalated to a senior engineer. One candidate feature is whether the ticket was submitted outside office hours. Over 400 past tickets:

To screen the feature, compute its mutual information with the target. Write $X$ for the feature and $Y$ for the target. Then $p(x, y)$ is the probability of a table cell, and $p(x)$ and $p(y)$ are the probabilities of a single row or a single column on its own:

$$I(X; Y) = \sum_{x}\sum_{y} p(x, y)\,\log_2\!\frac{p(x, y)}{p(x)\,p(y)}$$

The double sum runs over all four cells. Using $\log_2$ measures the result in bits. If $X$ and $Y$ were independent, every ratio inside the log would be $1$, and $I$ would be $0$.

What is $I(X; Y)$ for this feature, in bits?

Carry at least 6 decimal places through the working, and round your answer to 4 decimal places.