## 38. "Sensible" or "Sensitive"

On an English test, I had to translate a text into English. When translating one phrase, I wondered which word would be better to use: sensible (reasonable) or sensitive (perceptive). If I choose one of these words at random, I have a one in two chance of making a mistake. I could look at my neighbor's notebook, but from experience, I know that she makes mistakes on average one in five times with such translations. However, in this case, I would have a one in ten chance of being caught by the teacher for peeking at someone else's notebook - and that is three times worse than if I simply made a mistake.

What would you advise me, disregarding, of course, the moral aspect of the question: to copy from my neighbor or to randomly choose between the words "sensible" and "sensitive"?
38. Let $\alpha$ denote the measure of inconvenience associated with an incorrect translation. Without cheating, I risk making a mistake one out of two times (the measure of inconvenience being $\alpha$), which results in an average inconvenience of $\alpha / 2$. By cheating, I risk getting caught (the measure of inconvenience being $3 \alpha$) one out of ten times; I also risk making an incorrect translation (the measure of inconvenience being $\alpha$) if my neighbor is wrong and I am not caught by the teacher, which will happen with a probability of

$$
\text { 1/5.9/10=9/50. }
$$

The average risk in this case, therefore, is

$$
1 / 10 \cdot 3 \alpha+9 / 50 \cdot \alpha=24 / 50 \cdot \alpha
$$

This is slightly less than in the previous case ( $1 / 2 \cdot \alpha=$ $=25 / 50 \cdot \alpha)$.

Thus, from the adopted—immoral—point of view, it is preferable to cheat from a neighbor rather than choose a word at random.