Data Handling
Basic probability
Calculate theoretical and experimental probabilities for simple events and complements.
Probability measures how likely an event is, from 0 (impossible) to 1 (certain).
Fundamentals
\[ P(E)=\frac{\text{number of favorable outcomes}}{\text{number of equally likely outcomes}}. \]
Also: \(0\le P(E)\le1\).
Complement rule
\[ P(E')=1-P(E). \]
Combined events
- \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
- If independent: \(P(A\cap B)=P(A)P(B)\)
Experimental probability
\[ P(E)\approx\frac{\text{observed frequency}}{\text{number of trials}}. \]
Sample spaces and trees
Use sample-space tables or tree diagrams for multi-step outcomes. Multiply along branches, add across valid branches.
Exam strategy
- Define event clearly before calculating.
- Use fractions first; round at end if needed.
- Check complement and total probability sanity.
- Use diagrams to avoid missing outcomes.
Checkpoints
A fair die is rolled. Find \(P(\text{prime})\).
Answer: \(\frac{3}{6}=\frac12\) (2,3,5).
A bag has 4 red and 6 blue balls. Find \(P(\text{not red})\).
Answer: \(\frac{6}{10}=\frac35\).
For independent events, \(P(A)=0.3,P(B)=0.4\). Find \(P(A\cap B)\).
Answer: \(0.12\).
An event occurs 18 times in 50 trials. Estimate probability.
Answer: \(\frac{18}{50}=0.36\).
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