3.2 Probability 1

• Experimental and theoretical probability
• The probability scale
• Sample space and events
• Complementary events
• Combined events using tables and tree diagrams

• distinguish experimental from theoretical probability
• calculate the probability of a single event
• use the complement rule
• find probabilities of combined events using tables and tree diagrams
• appreciate the use of probability in decision making

“How do you measure how likely something is?”

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1. Measuring chance
   40 min · 2 practice tasks · quiz
   Putting a number on likelihood, and the difference between theory and experiment.
2. Combined events
   40 min · 2 practice tasks · quiz
   Two things happening together, using possibility tables and tree diagrams.
3. The probability scale and the language of chance
   40 min · 1 practice tasks · quiz
   Place events on the 0 to 1 line, and replace vague words such as probably with a number everyone can share.
4. Equally likely outcomes and fairness
   40 min · 1 practice tasks · quiz
   Theoretical probability divides by the number of outcomes only when those outcomes are equally likely.
5. Sample space and events
   40 min · 1 practice tasks · quiz
   List every outcome in a sample space, then name an event as a subset of that list.
6. Experimental probability as relative frequency
   40 min · 1 practice tasks · quiz
   Relative frequency is times-it-happened over trials; it wobbles in small samples and settles as the trials grow.
7. The complement: not A, and at least one
   40 min · 1 practice tasks · quiz
   P(not A) is 1 minus P(A). "At least one" is usually 1 minus the probability of none.
8. Mutually exclusive events and the addition rule
   40 min · 1 practice tasks · quiz
   If two events cannot happen together, P(A or B) is P(A) plus P(B); if they overlap, adding counts the overlap twice.
9. Possibility tables for two trials
   40 min · 1 practice tasks · quiz
   A grid of equally likely cells turns questions about two dice, two spinners or a coin and a die into counting.
10. Independent events: multiply along a tree
    40 min · 1 practice tasks · quiz
    If one trial does not change the next, multiply the probabilities. Replacement keeps a bag independent.
11. Dependent events: drawing without replacement
    40 min · 1 practice tasks · quiz
    If an item is not put back, the second fraction changes; multiply along the new branches.
12. Probability in decisions: games, weather and risk
    40 min · 1 practice tasks · quiz
    Use a calculated probability, not a hunch, when a game, a weather call or a premium is on the table; most betting games are unfair.