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Math 2HonorsName ________________________Lesson 4-1: Probability DistributionsLearning Goals: I can define and/or identify the following: event, sample space. I can calculate the probability of an event.I can determine when a frequency table is an appropriate display for a set of data.I can construct a frequency table for the data using the appropriate categories for each variable.Because of the symmetry in a fair die – each side is equally likely to end up on top when the die is rolled. Suppose a red die and green die are rolled at the same time. What does the entry “3, 2” in the chart mean?2019300335280Complete a copy of the chart below, showing all possible outcomes of a single roll of two dice. 466725182245How many possible outcomes are there?What is the probability of rolling a (1, 2), that is, a 1 on the red die and a 2 on the green die? What is the probability of rolling a (2, 1)? What is the probability of rolling a (4, 4)? Would the chart be any different if both dice had been the same color? Explain.The chart you completed in problem 1 is called a sample space for the situation of rolling two dice. A sample space is a list of all possible outcomes. For fair dice, all 36 outcomes in the sample space are equally likely to occur. Equally likely means that each outcome has the same probability. When outcomes are equally likely, the probability of an event is given by If two dice are rolled, what is the probability of getting doubles?a sum of 7?a sum of 11?a 2 on at least one die or a sum of 2?doubles and a sum of 8?doubles or a sum of 8?Suppose two dice are rolled.What is the probability that the sum is no more than 9?What is the probability that the sum is at least 9?What is the probability that the sum is 2 or 3? Is greater than 3? Is at least 3? Is less than 3?A frequency table shows all possible outcomes and the number of times they occur. A probability distribution shows all possible outcomes and the probability that they occur. Fill in the table below creating a frequency table and probability distribution. Sum23456789101112Total FrequencyProbabilityHow could you use the probability distribution table to find the probability that the sum of two dice is less than 3? Suppose you roll two dice and record the absolute value of the difference of the two numbers. Create a frequency table and probability distribution for this situation.Absolute Value of the DifferenceTotalFrequencyProbabilityWhat is the probability that the absolute value of the difference is 3?What is the probability that the absolute value of the difference is 2 or 3?What is the probability that the absolute value of the difference is no more than 3?What is the probability that the absolute value of the difference is more than 3?If you flip a coin, {heads, tails} is a sample space, but not a probability distribution. Create a probability distribution table by recording the number of heads as your outcome. Now suppose that you flip a coin twice. Complete a chart that shows the sample space of all possible outcomes. Create a table that shows each possible outcome, their frequencies for each outcome, and the probability they occur. What is the probability that you get exactly one head if you flip a coin twice? What is the probability that you get at least one head if you flip a coin twice? ................
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