Probability

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A random experiment is an experiment that: 1. Can be repeated any number of times under identical conditions 2. All possible outcomes are known in advance 3. The actual outcome cannot be predicted bef

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Sample Space (S): The set of all possible outcomes of a random experiment. For tossing three coins: S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} n(S) = 8 Each element is called a sample point.

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Equally likely events: Outcomes that have the same chance of occurring based on available evidence. Example: Drawing a card from a well-shuffled deck of 52 cards • All 52 cards are equally likely to

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Mutually Exclusive Events: Two or more events that cannot occur simultaneously. If one occurs, others cannot occur in the same trial. Mathematically: E₁ ∩ E₂ = ∅ Example: Rolling a die • Event A: Ge

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Exhaustive Events: A set of events is exhaustive if their union equals the sample space. At least one of them must occur. Mathematically: E₁ ∪ E₂ ∪ ... ∪ Eₙ = S Example: Rolling a die • Event A: Get

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Classical Definition of Probability: P(E) = Number of favorable outcomes / Total number of equally likely outcomes P(E) = m/n Range: 0 ≤ P(E) ≤ 1 Special cases: • P(impossible event) = 0 • P(certain

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Sample space: S = {1, 2, 3, 4, 5, 6}, n(S) = 6 (a) P(odd number): Favorable outcomes = {1, 3, 5} P(odd) = 3/6 = 1/2 (b) P(number > 4): Favorable outcomes = {5, 6} P(>4) = 2/6 = 1/3

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Sample space: S = {HH, HT, TH, TT} n(S) = 4 Event E: Exactly one head Favorable outcomes = {HT, TH} n(E) = 2 P(exactly one head) = 2/4 = 1/2