3.2 Probability II

• perform experiments involving probabilities in different situations
• identify the range of probability in different situations
• generate probability space of different events
• determine the probability of mutually exclusive and independent events
• determine probability of different events using tree diagrams
• appreciate the application of probability in real-life situations

“How is probability applied in real-life situations?”

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1. What probability means
   40 min · 1 practice tasks · quiz
   Explain probability as a measure of how likely an event is and use chance words.
2. Carrying out an experiment
   40 min · 1 practice tasks · quiz
   Toss a coin many times and compare the relative frequency with the theoretical probability.
3. Throwing a die
   40 min · 1 practice tasks · quiz
   Use the six equally likely outcomes of a die to find probabilities.
4. The range of probability
   40 min · 1 practice tasks · quiz
   State that every probability lies between 0 and 1 and test whether a value is possible.
5. The probability space
   40 min · 1 practice tasks · quiz
   List all the possible outcomes of an experiment to form its probability space.
6. Events and favourable outcomes
   40 min · 1 practice tasks · quiz
   Find probabilities from a probability space with equally likely outcomes.
7. The complement of an event
   40 min · 1 practice tasks · quiz
   Find the probability that an event does not happen using P(not E) = 1 - P(E).
8. Two coins
   40 min · 1 practice tasks · quiz
   List the four outcomes of tossing two coins and find probabilities from them.
9. The sum of two dice
   40 min · 1 practice tasks · quiz
   Use the thirty-six outcomes of two dice to find the probability of each sum.
10. Mutually exclusive events
    40 min · 1 practice tasks · quiz
    Recognise events that cannot happen together and find the probability of either.
11. The addition rule
    40 min · 1 practice tasks · quiz
    Add the probabilities of mutually exclusive events to find the chance of either.
12. Events that overlap
    40 min · 1 practice tasks · quiz
    Use P(A or B) = P(A) + P(B) - P(A and B) when two events can both happen.
13. Independent events
    40 min · 1 practice tasks · quiz
    Recognise events where the result of one does not affect the other.
14. The multiplication rule
    40 min · 1 practice tasks · quiz
    Multiply the probabilities of independent events to find the chance that both happen.
15. With and without replacement
    40 min · 1 practice tasks · quiz
    Compare independent draws with replacement and dependent draws without replacement.
16. Tree diagrams for one event
    40 min · 1 practice tasks · quiz
    Draw a tree diagram for a single event and read the branch probabilities.
17. Tree diagrams for two events
    40 min · 1 practice tasks · quiz
    Draw a tree for two events and list the four paths.
18. Multiplying along the branches
    40 min · 1 practice tasks · quiz
    Find the probability of a path by multiplying the branch probabilities.
19. Adding across the branches
    40 min · 1 practice tasks · quiz
    Add the probabilities of the paths that together make an event.
20. Drawing marbles from a bag
    40 min · 1 practice tasks · quiz
    Use a tree to find probabilities when two marbles are drawn without replacement.
21. Playing cards
    40 min · 1 practice tasks · quiz
    Use a pack of 52 cards to find probabilities, including overlapping events.
22. Probability in a weather forecast
    40 min · 1 practice tasks · quiz
    Use a tree to find the probability of rain over two days.
23. Fair games
    40 min · 1 practice tasks · quiz
    Decide whether a game of chance is fair using the expected return.
24. Expected numbers
    40 min · 1 practice tasks · quiz
    Find the expected number of successes using probability times the number of trials.
25. Probability: mixed review
    40 min · 1 practice tasks · quiz
    Bring together the range, spaces, mutually exclusive and independent events and trees.