The problem is related to nucleotides and genomes, but it's better to simplify it using dice.
EDIT 2: My original question wasn't very clear, so I've reworded it
I know that the probability of getting the 7-digit long sequence "4213433" if I throw a four-sided die 7 times is $\frac{1}{4^7}$
But, what is the expected occurrence of the sequence "4213433" if I throw a four-sided die $4.5 \times 10^6$ times?
EDIT 1: Okay, I think I found my answer. If I throw a four-sided die $4.5 \times 10^6$ times, the sequence 4213433 will occur randomly $\frac{4.5 \times 10^6}{4^7}$ or 274.658 times. Is that correct? EDIT 3:Almost. Like @joriki said in the comments, the exact answer would be $\frac{4.5 \times 10^6 - 6}{4^7}$