i need clear and complete answer 1. [10 points] Three-sided Die. Consider a sing
ID: 3354177 • Letter: I
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i need clear and complete answer
1. [10 points] Three-sided Die. Consider a single roll of a three-sided die, with sides labeled "Red", "Green", and "Blue". Assume each outcome is equally likely and specify a probability model for this roll of a die: (a) [1 point] write the sample space . (b) [1 point] Write the collection of events F (c) [1 point] Write the probability measure P (d) 13 pointsj Pick any one of the outcomes you listed in part (a) and explicitly interpret it (e) [4 points] Pick any one of the events you listed in part (b) and derive the corresponding (Hint: there should be 23 =8 events.) (Hint: remember to specify a probability for every event) in terms of a single roll of the die. (For example, with a coin toss: "The outcome Heads occurs when the coin lands heads up.") probability you calculated in part (e) by explicitly stating the assumption(s) and/or probability axiom(s).Explanation / Answer
a.The sample space is a set of all possible out comes.
hence in a single roll of a 3 sided die , the sample space is {red,green,blue}
b.The total number of events that are possible are
{red,green,blue, red-green,red-blue, blue-green,0,red-blue,green)
c).since all the colors are equally likely to appear, the possible outcome of each will be 1/3.
d). The probability of appearance of any given color is same and there are three colors. Hence the probability of occrance of each color is 1/3 .This means that on an average in three throws, each color is likely to appear once.
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