1. Multi-Stage Events and Applications of Probability
PB2
Multi-Stage Events and Applications of Probability

2. Basic concepts: Working out the number of expected outcomes
Construct and use tree diagrams for multiple-stage events
Establish the number of ordered OR unordered selections possible from a group of items
Use the formula for probability
Calculate the expected number of times an event will occur
Compare theoretical and experimental probabilities
Calculate the expected value of an event

3. Multi-stage events
Theory Book

4. Theory Book

10. Number of Arrangements
Theory Book
The fundamental counting principle states that if we have ‘p’ outcomes for first event and ‘q’ outcomes for the second event, then the total number of outcomes for both events is p × q. It simply involves multiplying the number of outcomes for each event together.
A coin is tossed and a die is rolled. How many different outcomes are possible?
There are two different outcomes for the coin toss and six different outcomes for the die roll.
Number of outcomes 2 × 6 = 12

16. Ordered Selections
Theory Book
An ordered selection or a permutation occurs when a selection is made from a group of items and the order is important. The order of the items in the selection is critical. AB is different to BA.
On your calculator: nPr (n items available for selection and r items to be selected in order).

21. Unordered Selections
Theory Book
Unordered selections or a combination occurs when a selection is made from a group of items and the order is not important. AB is the same as BA.
On your calculator: nCr (n items available for selection and r items to be selected).

27. Heading
Theory Book
The probability of two independent events occurring is equal to the product of the probability of each event. To calculate the probability of two events occurring on a tree diagram, multiply the probabilities along each successive branch.

34. Probability trees: Addition rule
Theory Book
Probability trees: Addition rule
The probability of one event or a second event is equal to the sum of the probabilities of each event. For example, when two unbiased coins are tossed the probability of throwing two heads or two tails is equal to the sum of the probabilities of two heads and two tails or = 0.50.

41. Expected Outcomes
Theory Book
The expected outcome is the number of times the outcome should occur. It may not equal the actual results.

47. Expected Value
Theory Book
Expected value indicates the expected outcome to be achieved in an event. It is calculated by multiplying each outcome by its probability and then adding all these results together.
Financial expectation is the expected value when the event involves money. The financial outcome is positive if money will be won and negative if money will be lost.

48. Theory Book

49. Theory Book