Two person have 16 and 32 dollars, respectively

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Two person have 16 and 32 dollars, respectively. They bet one dollar on the outcome of each of 900 independent tosses of a fair coin. What is an approximation to the probability that neither person is in debt at the end of the 900 tosses?

I tried to calculate using intersection probability of such: sum ncr(900,x)*0.5^900, x = 434 to 458 and get 0.578 but it didn't workout.

Result should be 0.6124.