Question

You roll 2 dice. What is the probability that the sum of the dice is odd or 1 die shows a 4?

Answer 1

`=>P("the sum of the dice is odd or 1 die shows a 4") =1/2 + 11/36 = 29/36`

Explanation:

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`