 Hello and welcome to this session. In this session, we will discuss about lightly, unlikely, neither likely nor unlikely events. Suppose you are going to school. If someone asks you, will you study in your class today? Then, your answer will be yes, you are quite certain that you will study at school today. Now again, if someone asks, will most of the class students will be absent today? Your answer will be no. It is unlikely for most of the students to be absent today. So, in our daily life, we can think of what can happen and what cannot. There are many situations in life where we consider the change or likelihood of something happening. Consider the following statements. First, we will probably buy a new TV soon. Second, I am almost certain that I will pass the examination. Third, it is likely that students will damage the prep. Fourth, it is unlikely that our students will win today. In these statements, each word that is probably certain, likely, unlikely, describes the probability. So, we can say that probability is to deal with likelihood of chance of events occurring. Consider the following statements and the first statement is, Tim, who is my sleeping, will be awake in next 24 hours time. Now, it is very likely that Tim will be awake in next 24 hours. It means the chances are very high. Therefore, it is a likely event. It will snow tomorrow. It depends on the season of the year. It means the chances are very less so. So, we can say it is an unlikely event. The next person entering the classroom in a co-educational school will be a male. Here, both male and female has equal chances of entering the room. It is a 50-50 chance. So, we say it is neither likely nor unlikely event. Now, in this statement, a man lives for 500 years and we know that this event cannot occur. No man can live for 500 years. So, this is an impossible event. The next statement is, in rolling a die, you will get a number less than 7. In rolling a die, it is certain that number we get will be one of the numbers from 1, 2, 3, 4, 5 and 6. Which are all less than 7. So, we can say it is a certain or sure event. Mathematically, we can say that probability of an event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood of probability. Near 0 indicates an unlikely event, probability around 1 by 2 indicates an event that is neither likely nor unlikely. And a probability near 1 indicates a likely event. We can represent probabilities on a number line as shown. An unlikely event would have a probability between 0 and 1 by 2. It would be near to 0. A likely event would have a probability between 1 by 2 and 1. And it would be near to 1 probability for neither likely nor unlikely event will be 1 by 2 or around 1 by 2. Here, at this point or around this point, a certain event has probability of 1 and an impossible event has 0 probability. Let us take an example. Look at this probability line. The probabilities of the events A, B, C and D have been marked on the line. Now we shall take descriptions of 4 events 1 by 1 and match them up with the letters A, B, C and D on this line. Now the first event is usually an unbiased dice and bit an even number. Now we know that there are odd or even numbers in dice. So both have equal chances of coming. So we can say it is neither likely nor unlikely event. We know that neither likely nor unlikely event has probability 1 by 2 or around 1 by 2. So it matches B that is 1 by 2. Next we have Christmas date even the next 12 months. It is certain that in a year that is 12 months Christmas will come that is it is a certain event which has the probability 1. Therefore it matches C. Now we have another event which says you pick a card from a normal pack of cards and get an Ace. We know that there are 52 cards in a pack and to choose an Ace card out of these 52 cards is unlikely but not impossible. So its probability is near to 0 therefore it matches A. Now we have another event which says seen that 5 sweets he will eat 1 sweet today. It is almost certain that seen will eat at least 1 sweet today. So probability is almost near to 1. We can say it is a likely event since its probability is near to 1 therefore it matches B. Thus we have seen how we can represent probabilities on the number line. This completes our session. Hope you enjoyed this session.