Question

Two dice are thrown simultaneously.Find P(sum of two no. is 7),P+sum of two no. is at least 3),P(sum of two no. is 1),P(same no.)

Answer 1

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}
n(s)=36
Let A={(1,6)(2,5)(3,4)(4,3)(5,2)(6,1)}
n(A)=6
p(A)=n(A)/n(S)=6/36=6
Let B={(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}
n(B)=35
p(B)=n(B)/n(S)=35/36
LetC={}
n(C)=0
p(C)=n(C)/n(S)=0/36=0
Let D={(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)}
n(D)=6
p(D)=n(D)/n(S)=6/36=6