Total number of outcomes# = "(Outcomes in 1 die)"^"(number of dice)" = 6^2 = 36#
#"Sample space(sum of dies)" = {3,5,7,9,11}#
Possibilities
#(1,2)
(2,1)
(1,4)
(4,1)
(2,3)
(3,2)
(1,6)
(6,1)
(2,5)
(5,2)
(3,4)#
#(4,3)
(3,6)
(6,3)
(4,5)
(5,4)
(6,5)
(5,6)#
#n("possibilities of odd sum" ) = 18#
#P"(Odd sum)" = 1/2#
#"Probability that none of the dices are showing 4 " =( 5/6)^2 = 25/36#
#"Probability that one of the dices are showing 4 " = 1 -( 5/6)^2 = 1 - 25/36 = 11/36#
#P("the sum of the dice is odd or 1 die shows a 4") = P"(Odd sum)" + P("one of the dice are showing 4 ")#
#=>P("the sum of the dice is odd or 1 die shows a 4") =1/2 + 11/36 = 29/36#