I was wondering how many SNPs there are in a single person on average
A SNP is a polymorphism in the population, it is not a thing a haplotype can carry. Each individual has a given variant for any given of the SNPs (except for cases of sequence deletion).
It is possible though to say how many SNP a diploid individual in between its two haplotypes but I doubt this is where you interest was. Ewens smapling formula gives expectation and distribution under an infinite alleles model, panmictic population and absence of selection.
Other statistics that make sense include the average number of deleterious mutations pre individual or a few other things or how many new mutations a couple transmit to their offspring,... But asking how many SNPs an individual carry on average makes little sense.
Note as @Chris said, by stating 10k SNPs in the human genome, you seem to under-estimate the number of SNPs.
In the comments, you further
Would it make more sense to consider a rough minimum and maximum?
The answer is no, it would not make more sense. Consider the definition of SNP by wikipedia
A single nucleotide polymorphism, often abbreviated to SNP (pronounced snip; plural snips), is a variation in a single nucleotide that occurs at a specific position in the genome, where each variation is present to some appreciable degree within a population [My emphasis]
The term population is key here. The concept of SNPs (or of polymorphism to be more general) makes only sense if you can make comparisons. A single individual does not have any polymorphism (to the exception of the one between his two sets of chromosomes).
If we step back and think of different species it might become more intuitive. Think of the number of pairwise differences between two species. It does not make any sense to ask "how many pairwise differences is there between a blue whale?" You need to say "how many pairwise differences is there between a blue whale and a wolf". Similarly, you cannot say "How many SNPs is there 'between a single individual'" (to the exception again of the consideration of the differences between the two sets of chromosomes), you need to consider a group of individuals.