Probability of at least once over five chances at variable odds each time

Question

If you had five chances to succeed in a game of chance, and you only needed one success to win, what would be your odds of winning that game of chance given that each try had the following different probabilities: 50%, 45%, 40%, 35%, and 30%; furthermore, what is the formula used to calculate this scenario should the variables change?

Answer 1

P(1 or more wins) = .5 + (.5)(.45) + (.5)(.55)(.4) + (.5)(.55)(.6)(.35) + (.5)(.55)(.6)(.65)(.3)

p₁ + (1-p₁)p₂ + (1-p₁)(1-p₂)p₃ + ...

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