I followed the same path using the same logic. Please explain, why am I getting different answer.I ain't getting 1.647.

1.5*ln(3)=1.098. Please someone explain. Silly thing though.😁

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Number of probes in unsuccessful search = $\displaystyle \frac{1}{1-x}$

Number Of Probes in successful search = $\displaystyle \frac{1}{x } * \ln \displaystyle \frac{1}{1-x}$

where x= load factor of hash table

since, x = $\displaystyle \frac{n}{m }$

Therefore using above formula , x= $\displaystyle \frac{2}{3 }$ , as no. of probes in unsuccessful search= 3.

Now using x=$\displaystyle \frac{2}{3 }$ , no of probes for successful search = $\displaystyle \frac{3}{2 } * \ln3$ = 1.647

Number Of Probes in successful search = $\displaystyle \frac{1}{x } * \ln \displaystyle \frac{1}{1-x}$

where x= load factor of hash table

since, x = $\displaystyle \frac{n}{m }$

Therefore using above formula , x= $\displaystyle \frac{2}{3 }$ , as no. of probes in unsuccessful search= 3.

Now using x=$\displaystyle \frac{2}{3 }$ , no of probes for successful search = $\displaystyle \frac{3}{2 } * \ln3$ = 1.647