Topic 2

Topic 2

1. Objectives: The approach to decision making, satisficing, and other alternatives to the rational approach. Calculation and interpretation of probabilities. Construction and analysis of decision trees as an aid to decision making. Calculation and interpretation of expected values and their use in decision analysis.

   • Rational/optimal decision making: Systematic step by step method in which hard quantitative data through observation or mathematical (statistical) analysis or modelling is used for making long term decisions. This approach attempts to find the best possible available alternative (e.g medical diagnosis)
     • Satisficing: is a decision making strategy that entails searching through the available alternative until an acceptability threshold is met. satisficing = combination of satisfy and suffice. We can't always optimse as we don't all the information associated with each putcome (bounded rationally) e.g choosing from a menu.
   • How can we weigh up different outcomes? The "laws of chance" under pin many decisions that are made in real life. We need an understanding of probability.
     • Prbability = chance; Probability is measured on a sliding scale. from 0 (impossible) to 1 (certain), what is the probability that i'll die? what is the probability that i'll be home after 8.30pm tonight.
       • Classical approach: P(A) = number of outcomes representing event A / total number of possible outcomes, where all of the outcome are assumed to be equally likely. Example 1 what is the probability of obtaining an odd number score on one throw of a dice? P(odd number score) = 3/6=0.5. Example 2 What is the probability of throwing a 6 on 1 roll of a dice? P(6)=1/6=0.16
       • Empirical= based on observed data: Requires past, or experimental data: P(A) = number of times event A occurred / total number of observations, Example out of 200 light bulbs manufactured on a particular day 15 were faulty, p(light bulb manufactured on given day is faulty) = 15/200 = 0.075
     • Subjective: a person uses judgement to asses the probability, example "i estimate that there will be 0.9 probability that this product will make a profit next year"
   • Mutually exclusive: two or more events are said to mutually exclusive " if the occurrence of one of the events means that the simultaneous occurrence of the other event is impossible. In other words both events cannot happen at the same time. Examples turning left and turning right, tossing a coin - heads and tails are mutually exclusive.
     • Mutually exhaustive: two or more events are said to be mutually exhaustive if they represent all possible outcomes. examples heads and tails in the toss of a coin, 1,2,3,4,5,6 as the outcome in the roll of a dice.
       • The addition rule (when we see OR): this gives the probability of either one event or another occurring, P(A or B) = P(A) + P(B) - p(A and B), if the events are mutually exclusive then P(A or B) = P(A) + P(B)
         • Example: one card is drawn from a well shuffled pack, find the probability that it is(1) either an ace or a king: (2) either a king or a heart. (1 the events "ace" and "king" are mutually exclusive so: p(ace or king)= 4/54 + 4/52 = 8/52, (2) the events "king" and "heart" are not mutually exclusive so:p(king or heart) = 4/52 +13/52 - 1/52 =16/52
   • Independent events: two events A and B are independent if the probability of A occurring is not affected by the occurrence of B, example P (it will rain in Cork on a certain day) is independent of whether that day is a week day or not, but is not independent of what month that day occurs in, as some months are rainier than others.
     • Conditional events: this is denoted by P(A|B) by which means "the probability of A occurring given that B has occurred. example a supermarket manager might judge P(delivered goods are in good condition) = 0.9 but P(delivered goods are in good condition | packaging is damaged) =0.3
       • Multiplication rule - independent events (when we see and) this gives the probability of one event and another event occurring. if the events are independent then P(A and B) =P(A) * P(B) example 1 if you toss a coin twice then the probability of getting two heads is = 0.5*0.5=o.25, since the two events are independent. example 2 probability of getting a 3 when you roll a dice is 1/6 =0.16, probability of getting two 3s when you roll a dice twice is 0.16*0.16 = 0.0256. the events are independent.
         • Multiplication rule - dependent events: if two events are dependent then P)A and B) =P(A) * P(B|A) = probability of A)*(probability of B given A has occurred) example a box contains 100 spark plugs of which 20 are defective. if two plugs are to be sampled from the box without replacement what is the probability that they will both be defective? P(first and second plugs defective) =P(first plug defective)*P(second plug defective) = 20/100*19/99)=0.0384
   • Expected value