Suppose A1, A2, A3 are independent events (subsets of the sample space S). Suppose that each of them has probability 1/2, then what is the probability that at least two of them happen?
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Since they are independent, we can multiply their probabilities: $P(A_1 \cap A_2 \cap A_3) = P(A_1) \cdot P(A_2) \cdot P(A_3) = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8}$ Now, let's find the probability that exactly two of them happen. There Show more…
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