Hey MN1987.

You can't use the binomial exactly if you are looking at consecutive streaks since the binomial only looks at getting n successes and it doesn't care about the order of the way that you get it.

Basically you need to consider the number of possibilities of getting 50 or more consecutive free throws. Now with 350 you will have at maximum 6 sets of a streak of 50 at the most and one streak of 350 at the minimum (in terms of streaks).

Can you explain where you got that formula from and how it was derived?