Random Experiments & Events 🧪

1. Random Experiment 🎲

An experiment where the outcome is uncertain and cannot be predicted with certainty.

• Tossing a Coin: Could be Head (H) or Tail (T).
• Rolling a Die: Could be 1, 2, 3, 4, 5, or 6.

2. Sample Space (S) 🌌

The set of all possible outcomes of a random experiment.

• Coin: S = {H, T}
• Die: S = {1, 2, 3, 4, 5, 6}

3. Event (E) 🎯

Any subset of the Sample Space. A specific result we are interested in.

• Event: Getting an Even number on a die.
• E = {2, 4, 6}

Types of Events 📋

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Other Types:

• Impossible Event: P(E) = 0. (e.g., Rolling a 7 on a standard die).
• Sure/Certain Event: P(E) = 1. (e.g., Rolling a number less than 7).
• Mutually Exclusive Events: Cannot happen together. (Discussed in next chapter).
• Exhaustive Events: Simple events that together cover the sample space.

Example

Experiment: Tossing two coins. Sample Space (S): {HH, HT, TH, TT} (Total 4)

Event A: Getting at least one Head. A = {HH, HT, TH}

Event B: Getting exactly two Tails. B = {TT}

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