Question

If you roll two dice and find their sum, what is the probability of the sum being even or greater than 8?

Answer 1

Answer 2

SOLUTION :

Events of even sum of two dice after rolling : 2, 4, 6, 8, 10, 12  : Total 6 events 

Probability of each event = 1/6 * 1/6 = 1/36 

P(even sum) = 6 * 1/36 = 1/6 .

Events of sum  greater than 8 are :  9. 10, 11, 12  : total 4 events 

Probability of each event = 1/6 * 1/6 = 1/36 

P(sum > 8) = 4 * 1/36 = 1/9 .

Two events , sum of 10 and 12 are common to both cases,

=> P(sum even AND sum > 8)  = 2 * 1/36 = 1/18 

So,

P( sum even OR sum > 8) 

= P(sum even) + P(sum > 8) - P(sum even AND sum > 8)

= 1/6 + 1/9 - 1/18

= 2/9 (ANSWER).

Answer 3

SOLUTION :

Events of even sum of two dice after rolling : 

(1, 1) , (1,3), (3,1), (2, 2) , (1, 5), (5,1), (2, 4), (4, 2), (3, 3) (2, 6), (6, 2), (3, 5), (5,3), (4,4) , (4, 6), (6, 4), (5, 5), 

(6, 6)  

Total 18 events 

Probability of each event = 1/6 * 1/6 = 1/36 

P(even sum) = 18 * 1/36 = 1/2.

Events of sum  greater than 8 :   (3, 6), (6, 3), (4, 5), (5, 4), (4, 6), (6, 4), (5, 5), (5, 6), (6, 5), (6, 6)  : 

Total 10 events 

Probability of each event = 1/6 * 1/6 = 1/36 

P(sum > 8) = 10 * 1/36 = 5/18 .

Events : (4, 6), (6, 4), (5, 5) and (6, 6) are common to both cases,

=> P(sum even AND sum > 8) : 4 * 1/36 = 1/9 

So,

P( sum even OR sum > 8) 

= P(sum even) + P(sum > 8) - P(sum even AND sum > 8)

= 1/2 + 5/18 - 1/9

= 2/3 (ANSWER).