Two 6-sided dice are rolled. Let X be the larger of the two numbers showing. For...

Two 6-sided dice are rolled. Let X be the larger of the two numbers showing. For each i from 1 to 6, find the probability that X = i.

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Expert Solution

Solution:

Given: Two 6-sided dice are rolled.

X = the larger of the two numbers showing.

For example: ( 2 , 1 ) then X = 2

( 3 , 3 ) , then X = 3

and so on.

Sample space of rolling of two dice is:

We have numbers from 1 to 6 on each die, then minimum possible value for X is 1 and maximum possible value would be 6.

Now we need to find counts for each largest number.

X=i	Outcomes:	f : frequency	Calculations:	P(X=i)
1	(1,1)	1	=1/36	0.0278
2	(1,2) , (2,2) , (2,1)	3	=3/36	0.0833
3	(1,3) , (2,3) , (3,3 ), (3,2 ), (3,1)	5	=5/36	0.1389
4	(1,4) , (2,4) , (3,4 ), (4,4 ) , (4, 3 ), (4, 2) ,(4 , 1)	7	=7/36	0.1944
5	(1,5) , (2,5) , (3,5 ), (4,5 ) ,(5,5 ) , (5, 4 ), (5, 3) ,(5 ,2), (5,1)	9	=9/36	0.2500
6	(1,6) , (2,6) , (3,6 ), (4,6 ) ,(5,6 ) ,(6,6) , (6, 5 ), (6, 4) ,(6,3) , (6 ,2), (6,1)	11	=11/36	0.3056
		N = 36

milcah answered 8 months ago

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