Identify the outcomes of each of the following events below of rolling 2 fair si
ID: 3134538 • Letter: I
Question
Identify the outcomes of each of the following events below of rolling 2 fair six sided die and calculate each event’s probability. State the probabilities as fractions. Note, “sum of dice” means to sum the number of dots on the up-faces of the two dice. a) Build the probability distribution for the sum of two dice (i.e. list the possible values of the random variable, X (sum of two dice) and each value’s corresponding probability) in table form. b) Event A is the sum of dice = 10 c) Event B is the sum of dice equaling 7 or 11. d) Event C is the same number on each die.
Explanation / Answer
Consider the table of possile results:
Hence,
a)
b)
Hence,
P(Sum = 10) = 1/12 [ANSWER]
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c)
From the table,
P(Sum = 7 or 11) = 1/6 + 1/18 = 2/9 [ANSWER]
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d)
There are 6 ways out of 36 to get the same number on both dice. So,
P(same) = 6/36 = 1/6 [ANSWER]
Die 1 Die 2 Sum 1 1 2 1 2 3 1 3 4 1 4 5 1 5 6 1 6 7 2 1 3 2 2 4 2 3 5 2 4 6 2 5 7 2 6 8 3 1 4 3 2 5 3 3 6 3 4 7 3 5 8 3 6 9 4 1 5 4 2 6 4 3 7 4 4 8 4 5 9 4 6 10 5 1 6 5 2 7 5 3 8 5 4 9 5 5 10 5 6 11 6 1 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12