Exercise 2: Four Independent Retry Attempts at 80% Success — Possible Solution
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GIVEN
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4 independent attempts, each succeeding with probability 0.8
(failure probability 0.2 per attempt).

STEP 1: PROBABILITY ALL 4 ATTEMPTS FAIL
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Per this chapter's own multiplication rule for independent events,
generalized to 4 events:

  P(all 4 fail) = 0.2 x 0.2 x 0.2 x 0.2 = 0.2^4 = 0.0016 (0.16%)

STEP 2: PROBABILITY AT LEAST ONE SUCCEEDS
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"At least one succeeds" is exactly the complement of "all fail," per
Chapter 2's own complement rule:

  P(at least one succeeds) = 1 - P(all fail) = 1 - 0.0016 = 0.9984
                                                            (99.84%)

WHY THIS WORKS AS AN ANSWER
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The all-fail probability is computed by directly multiplying the four
independent per-attempt failure probabilities together, per this
chapter's own multiplication rule, and the at-least-one-success
probability is derived from it using Chapter 2's own complement rule
rather than being computed as a separate, harder calculation from
scratch.