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Probability

General Rules

  • 0 鈮� 饾憙 鈮� 1
    • Probabilities are values between zero and 1.
    • They CANNOT be:
      • Negative
      • Greater than 1
    • They CAN be:
      • Fractions
      • Decimals
      • Percentages
  • P(E) = \( \frac{n(E)}{n(S)} \)
    • To find the probability of an event (E), count the number of times the event happens and divide by the total number of outcomes in the sample space (S)

Addition Rules

  • 饾憙(饾惛)+饾憙(饾惛饾憪) =1 or 1鈭掟潙�(饾惛) =饾憙(饾惛饾憪)
    • The complement of an event is the probability that event does NOT
      happen.
    • Two complements add up to 100% or 1.
  • OR
    • Mutually Exclusive
      • Two events that do NOT happen at the same time.
      • 饾憙(饾惛 饾憸饾憻 饾惞)=饾憙(饾惛)+饾憙(饾惞)
    • NOT Mutually Exclusive
      • Two events that DO happen at the same time.
      • 饾憙(饾惛 饾憸饾憻 饾惞)=饾憙(饾惛)+饾憙(饾惞)鈭掟潙�(饾惛 饾憥饾憶饾憫 饾惞)

Multiplication Rules

  • AND
    • Independent
      • Two events that are NOT affected by each other.
      • 饾憙(饾惛 饾憥饾憶饾憫 饾惞)=饾憙(饾惛)脳饾憙(饾惞)
    • Dependent (aka NOT independent)
      • Two events that ARE affected by each other.
      • 饾憙(饾惛 饾憥饾憶饾憫 饾惞)=饾憙(饾惛)脳饾憙(饾惞|饾惛)
  • Fundamental Counting Principle
    • If multiple independent events happen consecutively, the total number of outcomes is found by multiplying the events.
      • 饾憳1&迟颈尘别蝉;饾憳2&迟颈尘别蝉;饾憳3&迟颈尘别蝉;鈥︷潙�n
  • Conditional Probabilities
    • 饾憙(饾惞|饾惛) = \( \frac{P(E \text{ and } F)}{P(E)} \)
    • The sample space changes based on the condition that is applied.
    • Key words to look out for:
      • If
      • Given that
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