Let (Ω, F , P) be a probability space. Suppose that Ω is the collection of...

Let (Ω, F , P) be a probability space. Suppose that Ω is the collection of all possible outcomes of a single iteration of a certain experiment. Also suppose that, for each C ∈ F, the probability that the outcome of this experiment is contained in C is P(C).
Consider events A, B ∈ F with P(A) + P(B) > 0. Suppose that the experiment is iterated indefinitely, with each iteration identical and independent of all the other iterations, until it results in an outcome that is an element of A ∪ B, after which it stops. What is the probability that this procedure results in an outcome that is an element of A? Do not use conditional probability to answer this question.

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orchestra answered 1 year ago

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