Part of ALG-04 — Probability & Distributions

Previous Year Analysis

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Most tested topics (2020-2024):

  1. Bayes' theorem (bags, machines, defective items)
  2. Binomial distribution (finding probabilities, mean/variance)
  3. Complement method (at least one success)
  4. Conditional probability (given information, restricted sample space)
  5. Classical counting (balls, cards, dice)

Difficulty distribution:

  • 30% easy (direct formula, complement)
  • 50% medium (Bayes', binomial computation)
  • 20% hard (multi-step conditional, parameter finding)

Time targets:

  • Basic probability (complement, addition rule): 1-2 minutes
  • Conditional/Bayes': 2-3 minutes
  • Binomial computation: 2-3 minutes
  • Complex multi-step: 3-4 minutes

Recurring patterns:

  • "A ball drawn from one of several bags" → Bayes'
  • "n independent trials, P(at least k)" → Binomial + complement
  • "Given that event A occurred, find P(B)" → Conditional
  • Truth-teller/liar + dice → Bayes' classic

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