 Hello and welcome to the session. In this session we will analyze decisions and strategies using probability concepts. Now we know that decision theory helps various organizations in making decisions. Decision making contains both psychological and rational factors. Now decision making is defined as a process of selecting that act from the set of alternatives which is supposed to meet objectives up to the satisfaction of the decision maker. Now let us see the main components of decision making. First is number of events or states of nature. Second is number of possible acts. There is the consequence, value or payoff to the decision maker of taking any of the available actions in the light of the possible states of nature. And next is the criterion by which decision maker judges between alternative acts. Now let us discuss some of the terms. First is, now in decision making programs the selection of a single act from a set of alternative acts is done. Now these acts are denoted by A1, A2, A3 and so on. Now let us discuss another term that is events or states of nature. Now the events, the occurrences which are not in the control of the decision maker and which determine the level of success for a given act. Now these are denoted by A1, A2 and so on. All these can be denoted by S1, S2 and so on. The next term is payoff. Now the result of combination of an act with each of the events is the outcome and the welfare purpose or loss of each such outcome is called payoff. Now here you can see its matrix form representation. Now in this matrix here we have little states of nature or events even E2 and so on up to EL. And here we have written acts that is A1, A2 and so on up to AK. Now this entry A11 shows the payoff of first event when first action or first act is chosen. So Aij is the payoff when jth act is chosen. So this matrix is called the payoff matrix. Now let us discuss types of decision making, the decision maker under circulating and second is decision maker under uncertainty. Now in first case the decision maker has complete knowledge of outcome of every decision choice with certainty. And in second case early payoffs are known and nothing is known about the likelihood of events. Now there are various approaches for decision making under uncertainty. All of them one is really satisfactory. First is maximum and maximum criteria. Now according to maximum criterion the decision maker should select the alternative which maximizes the minimum payoff he can get. And according to maximum criterion the decision maker should select the alternative which maximizes the maximum value of outcome. The second criteria is lack of criteria. Now according to this criteria if the probabilities of events are unknown they should be assumed equal and actions should be judged according to their payoffs. Average over all states of nature. Third is regret criterion. Now the regret outcome is the difference between the value of that outcome and the maximum value of all the possible outcomes in consideration to the particular chance event that actually occurred. The decision maker should select the alternative that minimizes the maximum weight loss he could suffer. Now we will discuss an example. Now here consider the possible payoff matrix where A1, A2 and A3 are the X and S1, S2 and S3 are the states of nature or the events. Now here no probabilities are known for the occurrence of the nature states and we have to compare the solutions obtained by each of the criteria. First is maximum criteria. Second is lackless criteria. Let us start with maximum criteria. Now here we will find the minimum payoffs for each of the following rows. Now in the first row you can see that minimum payoff is 2. In second row the minimum payoff is 7. And in third row from 6, 4 and 3 the minimum payoff is 3. Now according to maximum criterion we know that the decision maker should select the alternative which maximizes the minimum payoff he can get. So for this last column that is this column of minimum payoffs we will select the maximum value. So here the maximum value is 7. Now the decision maker should select this alternative which maximizes the minimum payoff he can get. So here the best action is A2. Now we will start this using lackless criteria. Now here we will assume each outcome will be equally likely. Now according to this criteria different actions should be judged according to their payoffs averaged over all the states of nature. So the average monetary payoff of action A1 denoted by e of A1 is equal to sum of observations that is 5 plus 2 plus 7 all upon number of observations that is 3. And on calculating this is equal to 4.7. Similarly the average payoff for action A2 is equal to 8 plus 7 plus 8 all upon 3. And on calculating this is equal to 7.7. Similarly e of A3 is equal to 6 plus 4 plus 3 all upon 3 that is equal to 4.3. Now from these three e of A2 is maximum that is average monetary payoff of action A2 is maximum. So best action is A2. So in this session we have analyzed the decisions and strategies using probability concepts. And this completes that session. Hope you all have enjoyed this session.