 Hello and welcome to the session. In this session we will use probabilities to make fair decisions. We know that probability is the measure of how likely it is for an event to occur. The probability of an event varies from 0 to 1. Now we will discuss how to use probabilities to make fair decisions. Now probability can be used to make decisions and predictions. We can use the probability of an event occurring to set up a proportion to find the number of times an event is likely to occur. A probability experiment is said to be fair if all its outcomes are equally likely or if the expected value of any random variable is 0. Or we can say a game in which the expected value for the player is 0. That is, there is no net gain or loss is said to be a fair game. Or a game involving chance is said to be fair if each player is equally likely to win. Now let us discuss an example from six students. In our team teacher has to choose one of them randomly to be the leader of the team. Now teacher A's plan is assign each student a number then spin this given spinner with six equal sectors. The leader is the student whose number is 1 and teacher B's plan is assign each student a number then toss three coins, select a player according to the given chart. That is if three heads appear then the student with number 2 is selected. If two heads followed by a tail appear then the student with number 1 is selected. Similarly we select the students with all given possible combinations of heads and tails. Now we shall check whether both the plans can be considered to be fair. First of all let us check teacher A's plan for fairness. Here we are given a spinner with six equal sectors that means each sector has equally likely possibility. So here the probability that the number 1 is spun is equal to 1 by 6 as the number of favourable outcome will be 1 and total number of outcomes are 6. So probability that number 1 is spun will be equal to 1 by 6. Similarly probability that number 2 is spun is equal to 1 by 6. Probability that number 3 is spun is equal to 1 by 6. Probability that number 4 is spun is also equal to 1 by 6. Probability that number 5 is spun is equal to 1 by 6 and the probability that number 6 is spun is equal to 1 by 6. This means each student has equal chance of selection as leader with probability of 1 by 6. So teacher A's plan is considered to be fair in the selection of a leader. Now we check teacher B's plan for fairness. The sample space of flipping three coins is given by the set containing H H H, H H T, H T H, H T T, T H H, T H T, T T H and T T T. Where H denotes the occurrence of head and T denotes the occurrence of tail, there are 8 outcomes which are equally likely. From the given chart we see that the number of favourable outcomes for student 1 is 2. So student 1 has probability 2 upon 8. Similarly number of favourable outcomes for student 2 is 2. Similarly student 2 has probability that is 2 upon 8 and rest all other players have one outcome. So they will have probability of 1 by 8 each. So here each student does not have an equal chance of selection as a leader of the team. Therefore teacher B's plan cannot be considered to be fair in the selection of leader. Thus in this session we have discussed how to use probabilities to make fair decisions. This completes our session. Hope you enjoyed this session.