A red die and a green die are rolled. What is the probability that the sum is odd?

Answer 1

Possible outcomes of 2 dice are

11

12

13

14

15

16 half are odd, half are even

same with

21

22

23

...

26 half odd half even

same with

31

32

33

...

36

same with

41

42

43

...

46

and with

51,

52

53,

...

56

and

61

62

63

...

66

6x6 = 36 outcomes, 18 are even sums, 18 are odd sums

Pr(odd sum) = 50%

Pr(even sum) = 50%

Answer 2

Possible outcomes of 2 dice are

11

12

13

14

15

16 half are odd, half are even

same with

21

22

23

...

26 half odd half even

same with

31

32

33

...

36

same with

41

42

43

...

46

and with

51,

52

53,

...

56

and

61

62

63

...

66

6x6 = 36 outcomes, 18 are even sums, 18 are odd sums

Pr(odd sum) = 18/36 = 50%

Pr(even sum) =18/36 = 50%

that exhausts the possibilities.

even and odd sums are mutually exclusive and exhaust the possible outcomes.

Probability of getting an odd sum is exactly 50%

Answer 3

The color of the die here is immaterial. In order to get a sum from two numbers to be odd, one needs to be odd and the other needs to be even. Since this is an "and" problem (not an "or"); you will need to multiply the two probabilities to answer the question. So, the probability of getting an even on one is 50% and the probability of getting an odd on the other is 50%.

1. 0.5(0.5) = .25; 25% chance of getting an odd sum with two dice rolled.

Make sense?