Question

Find the probability that the sum of score is even in a throw of two dice

Answer 1

Given

n(s)=36

{(1,1) (1,2)...(1,6)

(2,1) (2,2)..(2,6)

...  (6,6)}

sum is even =p{(1,1) (1,3) (1,5) (2,2) (2,4) (2,6) (3,1) (3,3) (3,5) (4,2) (4,4) (4,6) (5,1) (5,3) (5,5) (6,2) (6,4) (6,6)}=18

  probability(sum of score is even)=18/36

                                                         =1/2=0.5

Answer 2

Given,

2 dices are thrown simultaneously

To Find,

Probability that the sum of score is even = ?

Solution,

Possible outcomes when 2 dices are thrown are:

[ (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)]

Total possible outcomes = 36

Favourable outcome when score is even: [(1,1) (1,3) (1,5) (2,2) (2,4) (2,6) (3,1) (3,3) (3,5) (4,2) (4,4) (4,6) (5,1) (5,3) (5,5) (6,2) (6,4) (6,6)]

Total favourable outcomes = 18

Probability of getting an even sum of scores  = Favourable outcomes/ total outcomes

Probability of getting an even sum of scores  = 18 / 36

Probability of getting an even sum of scores = 1/2 = 0.5

Hence,  the probability that the sum of scores is even in a throw of two dice is  1/2