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156 Ganita Manjari | Grade 9 | Part I As you can see from the above example, probability deals with uncertainty or chance. One key feature of our increasingly complicated society is that we must deal with questions that have no fixed answer but rather one or more possibilities for the answer. Thus, understanding how to objectively estimate the probability of events is crucial in many aspects of life. In this chapter, we will learn how we can measure probability more objectively, i.e., the ways of collecting evidence that can be used for an objective estimate of likelihood. But first, we must understand a few terms and ideas such as randomness and the probability scale. 7.1.1 What is Randomness? Randomness refers to a situation or action (like the tossing of a coin or the rolling of a die) where you cannot predict exactly what will happen. Although you may know all the possible outcomes, you cannot say which one will definitely occur. For example, • Tossing a coin: You know it could be heads or tails, but you cannot be sure which one will come up in a single toss. • Rolling a die: You know the possible outcomes are 1, 2, 3, 4, 5, or 6, but you do not know which number will appear on a particular roll. These observations (commonly called experiments or trials in probability) are called random because of their unpredictability. The lucky draw example mentioned earlier is an example of a random observation or experiment, as the outcome cannot be predicted in advance, and each student has an equal chance of being selected. All you can say is what could happen, not what will happen. Random Observations: A random experiment is something you can repeat (like tossing a coin), where every time you do it, the result might be different and you cannot know the outcome in advance. Think and Reflect Such unpredictability can be useful sometimes! For example, in a cricket match, the fact that a coin is tossed to decide which team will bat first is considered to be a fair method. Can you explain why? Probability is the area of mathematics that studies randomness and how likely a specific outcome is to happen in a random situation. For example, when you toss a coin, the probability for heads is , and 2