### Probability of Rolling a Second Number Greater Than the First #### Problem Statement A single die is rolled twice. The 36 equally-likely outcomes are shown in the table below. Find the probability of getting a second number that is greater than the first number. #### Outcome Table The table shown to the right details each possible outcome of rolling a die twice. The outcomes are ordered pairs, where the first number represents the result of the first roll and the second number represents the result of the second roll. | | Second Roll | |---------|--------------| | | (1) | (2) | (3) | (4) | (5) | (6) | | **First Roll** | | | | | | | | (1) | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) | | (2) | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) | | (3) | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) | | (4) | (4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) | | (5) | (5,1) | (5,2) | (5,3) | (5,4) | (5,5) | (5,6) | | (6) | (6,1) | (6,2) | (6,3) | (6,4) | (6,5) | (6,6) | In this table: - The rows represent the possible outcomes of the first roll. - The columns represent the possible outcomes of the second roll. - Each cell in the table represents one of the 36 possible outcomes when rolling a die twice. #### Probability Calculation To find the probability of the second number being greater than the first number, identify the pairs where the second number is larger than the first. #### Answer

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Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.