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Find the probability distribution of the sum of the numbers obtained when two dice are thrown once.

Find the probability distribution of the sum of the numbers obtained when two dice are thrown once.

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
The sample space contains 6*6=36 elements
sum of elements on dice from 2,3,4,.,12
p(sum=2) =(1,1)= 1/36 ;p(sum=3) =(1,2)(2,1)= 2/36 ;
p(sum=4) = (3,1)(2,2)(1,3)=3/36
p(sum=5) = (1,4)(2,3)(3,2)(4,1)=4/36
;p(sum=6) = (1,5)(5,1)(2,4)(4,2)(3,3)=5/36
;p(sum=7) = (1,6)(6,1)(2,5)(5,2)(4,3)(3,4)=6/36
p(sum=8) = (2,6)(6,2)(5,3)(3,5)(4,4)=5/36
;p(sum=9) = (6,3)(3,6)(4,5)(5,4)=4/36
;p(sum=10) = (6,4)(4,6)(5,5)=3/36
p(sum=11) = (5,6)(6,5)=2/36 ;
p(sum=12) = (6,6)=1/36
Hence expectation=np
=2(1/36)+3(2/36)+4(3/36)+5(4/36)+6(5/36)+7(6/36)+8(5/36)+9(4/36)+10(3/36)+11(2/36)+12(1/36)
=7
Thanks and Regards
Shaik Aasif
askIITians faculty

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