3.2 Probability II

• Theoretical probability from a stated model: equally likely outcomes; sectors (angle / 360); a standard pack of cards
• Discrete probability distributions (probabilities add to 1; at most, at least, more than) and continuous uniform probability on an interval
• Laws of probability: the addition law; mutually exclusive events; independent events and the product test
• Tree diagrams without replacement; conditional probability on a branch; applications to surveys, forecasts and expected counts

• determine theoretical probability in different situations
• determine discrete and continuous probabilities in different situations
• apply laws of probability to predict likelihood of events
• determine probability of mutually exclusive and independent events
• calculate probabilities using tree diagrams
• appreciate the application of probability in day-to-day life

“How is the knowledge of probability important?”

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1. Theoretical probability needs a model
   40 min · 1 practice tasks · quiz
   Find a theoretical probability from equally likely outcomes, or from a measure such as an angle, and say when the equal-chance assumption is false.
2. Discrete probability
   40 min · 1 practice tasks · quiz
   Use a probability table for a countable variable, check that the probabilities add to 1, and read at most, at least and fewer than.
3. Continuous probability on an interval
   40 min · 1 practice tasks · quiz
   Find a probability as a fraction of an interval in a continuous uniform model, and give probability 0 to one exact instant.
4. The addition law
   40 min · 1 practice tasks · quiz
   Use P(A or B) = P(A) + P(B) - P(A and B), and drop the last term only when the events are mutually exclusive.
5. Independent events
   40 min · 1 practice tasks · quiz
   Test independence by the product rule, and see why mutually exclusive events with positive probability fail that test.
6. Choose the law
   40 min · 1 practice tasks · quiz
   Decide from the story whether to add, add and subtract the overlap, or multiply, and state the assumption when you multiply.
7. Tree diagrams and a changed chance
   40 min · 1 practice tasks · quiz
   Multiply along the branches of a without-replacement tree, add the paths that match the question, and read a second-branch probability as a given.
8. What a probability does not decide
   40 min · 1 practice tasks · quiz
   Apply mutually exclusive survey data, a complement and an expected count, and separate the calculation from a safety or election claim.