Number of probes in a successful search in open address hashing
You are almost right about &quot;5 probes&quot;. It will take, in fact, 6 linear probes to find an empty slot if the probe starts at index 0 of a table with slots 0 through 4 occupied (and slot 5 available). They are 5 failing probes and 1 successful probe at last.
However, you are, apparently, skipping the meaning of the word &quot;expected&quot;. That word here means &quot;on average&quot; basically.

While the number of probes can be as big as 4 sometimes, it can be as low as 1 many times as well. So it is not surprising the expected number of probes can be as low as 2.
To be exact and rigorous, the phrase &quot;expected number&quot; as in &quot;the expected number of probes&quot; and &quot;the maximum expected number of probes&quot; has a specific meaning defined in mathematical terms.

The expected value of a discrete random variable $X$ is $E[X]=\sum_xx\cdot \text{pr}\{X=x\}$, where $\text{pr}\{X=x\}$ is the probability of $X$ taking value $x$.

&quot;The expected number of probes&quot; is the shorthand for &quot;the expected value of the discrete random variable that stands for the number of probes.&quot; You can understand it simply as &quot;the average number of probes&quot;.
I would recommend you read sections in the textbook you are reading that introduce or review related concepts. Or section 3, Discrete random variables in Appendix C of the book CLRS.