Two fair 6-sided dice are tossed. Let X denote the number appearing on the first die...

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Two fair 6-sided dice are tossed. Let X denote the number appearing on the first die and let y denote the number appearing on

math Statistics-And-Probability

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Answer 1

Answer #1

total outcomes by rolling two dice =6² = 36

outcomes are

1,1	2,1	3,1	4,1	5,1	6,1
1,2	2,2	3,2	4,2	5,2	6,2
1,3	2,3	3,3	4,3	5,3	6,3
1,4	2,4	3,4	4,4	5,4	6,4
1,5	2,5	3,5	4,5	5,5	6,5
1,6	2,6	3,6	4,6	5,6	6,6

a single die has 6 outcomes

P(X=1) = 1/6

P(Y=1) = 1/6

P(X=1,Y=1) = 1/36

from here,

P(X=1,Y=1)=P(x=1) * P(Y=1)

similarly

P(X=2,Y=2)=P(x=2) * P(Y=2)

ans so on

so, it can be generalised as

P(X=x,Y=y) = P(X=x) * P(Y=y)

		Y
		1	2	3	4	5	6	P(X=x)
X	1	1/36	1/36	1/36	1/36	1/36	1/36	1/6
	2	1/36	1/36	1/36	1/36	1/36	1/36	1/6
	3	1/36	1/36	1/36	1/36	1/36	1/36	1/6
	4	1/36	1/36	1/36	1/36	1/36	1/36	1/6
	5	1/36	1/36	1/36	1/36	1/36	1/36	1/6
	6	1/36	1/36	1/36	1/36	1/36	1/36	1/6
	P(Y=y)	1/6	1/6	1/6	1/6	1/6	1/6	1

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Answer 2

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1,1	2,1	3,1	4,1	5,1	6,1
1,2	2,2	3,2	4,2	5,2	6,2
1,3	2,3	3,3	4,3	5,3	6,3
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1,5	2,5	3,5	4,5	5,5	6,5
1,6	2,6	3,6	4,6	5,6	6,6

1,1	2,1	3,1	4,1	5,1	6,1
1,2	2,2	3,2	4,2	5,2	6,2
1,3	2,3	3,3	4,3	5,3	6,3
1,4	2,4	3,4	4,4	5,4	6,4
1,5	2,5	3,5	4,5	5,5	6,5
1,6	2,6	3,6	4,6	5,6	6,6

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Two fair 6-sided dice are tossed. Let X denote the number appearing on the first die...

1,1	2,1	3,1	4,1	5,1	6,1
1,2	2,2	3,2	4,2	5,2	6,2
1,3	2,3	3,3	4,3	5,3	6,3
1,4	2,4	3,4	4,4	5,4	6,4
1,5	2,5	3,5	4,5	5,5	6,5
1,6	2,6	3,6	4,6	5,6	6,6