Question

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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 1 year ago
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