Guide me tutor. Thank you!

Scenario: A certain online game involves three battles done consecutively. Each battle can result into a Win, a Lose, or a Tie. Suppose you are interested in the number of times the battle results into a Win. Using the topics discussed in Chapter 1, analyze and explain the probability distribution of winning in battle. Follow all steps discussed and obtain the statistical measurements. Use the fractions obtained in solving. If you will use decimals, use three decimal places. . Use multiples of 0.05 in the vertical axis of the histogram.Submission Format: Performance Check 1 Scenario: .... Step 1: We are interested in... so we let.... Step 2: Next, we list the... Step 3: ... *Use your own words in explaining. Provide complete solutions Including appropriate diagrams (tree diagram), tables, formulas, set notations. labels, representations. and computations. - Analyze and Explore Activity 1. Two coins are tossed. Let X be the number of heads. a. List the sample space of the experiment. b. What are the possible values of X? In the previous module, we have learned to determine the values of a discrete random variable. We can make a frequency distribution of the values of the random variable and determine the probability that each value of the random variable will occur. Probabiliv Distribution ofa Discrete Random Variable The probability distribution of a random variable designates probabilities to the possible values of a random variable. How do we construct a probability distribution? Consider the situation in Activity 1. Step 1. List the sample space of the experiment. S = {HI-I, HT, TH, TT} Step 2. Assign the possible values in each outcome. Number of Heads Step 4. Construct the probability distribution of the random variable by getting the probability of occurrence of each value of the random variable. Number of Heads Number of Probability Occurrence The probability distribution of the random variable X can be written as: X 0 1 2 1'00 l E l 4 4 4 Activity 2. Examine the probability distribution above. a. What do you notice about the probability distribution? b. What is the sum of the probabilities of the random variable? Properties of :1 Discrete Probability Distribution 1. 0 S POD 5 1 The probabilities in a probability distribution are non-negative. The minimum value is O and the maximum value should be 1. 2. 2 P(X) = 1 The sum of the probabilities for all the possible values of a random variable is equal to 1. Let's verify whether the probability distribution in Activity 1 satises the properties of a discrete probability distribution. 1. i and}E are non negative numbers, so it satisfies the first preperty. 2. i+ E + i = 1. Therefore, it satisfies the second property. Graphical Representation of a Discrete Probability Distribution The probability distribution of a discrete random variable can be shown graphically by constructing a histogram. The graph is called a probability histogram. The probability histogram displays the possible values of a discrete random variable on the horizontal axis and the probabilities of those values in the vertical axis. Considering the probability distribution used above, let's construct its graphical representation. 0 A probability distribution of a discrete random variable is a correspondence that assigns probabilities to the values of a random variable. It is also called the probability mass function. e For any discrete random variable X, the following is true: a. 0 5 P00 5 1 b. 2 P(X) = 1 0 Probability distribution of a discrete random variable can also be represented through a graph using histogram. It is referred to as the probability histogram