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)

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)

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