CHAPTER 40 Probability

Probability What is Probability? PROBABILITY is how likely something is to happen. In any situation, the possible things that can happen are called OUTCOMES. An OUTCOME of particular interest is called an EVENT. Probability And Probability Scale A probability of 0 means that an event is IMPOSSIBLE A probability of 1 means that an event is CERTAIN Calculating Probabilities Using Equally Likely Outcomes Probabilities can be CALCULATED in situations where each outcome is EQUALLY LIKELY to occur. The probability of an event X occurring is calculated using: P (X) = Number of Favourable Outcomes Total Number of Possible Outcomes

Probability In many probability situations items are taken or picked at RANDOM. This means that any item is equally likely to be picked. Estimating Probabilities Using Relative Frequency Sometimes probabilities CANNOT be calculated using equally likely outcomes. In such situations probabilities can be estimated using the idea of RELATIVE FREQUENCY. It is not always necessary to perform an experiment or make observations, sometimes the information required can be found in past records. The relative frequency of an event is given by: Relative Frequency = Number of favourable outcomes in experiment/survey Total number of trials in the experiments/survey

Probability Mutually Exclusive Events MUTUALLY EXCLUSIVE EVENTS are events which CANNOT HAPPEN AT THE SAME TIME. When A and B are events which cannot happen at the same time: P(A or B) = P (A) + P (B) The Probability Of An Event Not Happening The events A and not A cannot happen at the same time. Because either ‘event A’ or ‘event not A’ is certain to happen: P (A) + P (not A) = 1 => P (not A) = 1 – P(A)

Probability Combining Two Events When two events take place at the same time all possible outcomes can be worked out by: a) Listing all the possible outcomes systematically b) Using a POSSIBILITY SPACE DIAGRAM c) Draw a TREE DIAGRAM

Probability Independent Events Two events are INDEPENDENT if the outcome of one event does not affect the outcome of the other event. When A and B are INDEPENDENT events then the probability of A and B occurring is given by: P (A and B) = P (A) x P (B) This rule can be extended to any number of INDEPENDENT events. For example: P (A and B and C) = P (A) X P (B) X P (C)