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

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

Multi-stage events Theory Book

Theory Book

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

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).

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).

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.

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 0.25 + 0.25 = 0.50.

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

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.

Theory Book

Theory Book