The problem assumes we randomly sample from a standard normal for 10 times. And ask the expected number of cases that the newly sampled number is the highest. It seems the relevant question has been discussed for the uniform, and the result has something to do with $\sum_{i=1}^n1/i$.
I wonder whether the same logic applies here. For example, the probability for the second sample to be larger than the first one is $1/2$, and the probability for the third sample to be larger than the first and the second one is $1/3$. I must miss out something as the information of having a standard normal is not used. Please advise. Thanks~~