This question is about performing a series of tests, each one randomly passing or failing with a known probability. Successes give you a point, fails take one away. The aim is to find out the overall likelihood of achieving a certain score at least once along the way.
Let's say we have -
n = number of tests,
p = probability of success in a test,
s = score required to pass the entire scenario.
Example: I have up to 100 coin flips to acquire a score of +10. Heads are +1 and tails are -1. If at any point i am at +10, the scenario is a pass. If i never reach +10, it's a fail. What would be the probability of passing the scenario here? (n=100, p=0.5, s=10)
If anyone can figure out the formula for this I'd be very grateful! I can't wrap my brain around this.