Question

Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is(ii) 13?(iii) less than or equal to 12?

Answer 1

if two dices are thrown, the total possible outcomes will be:
(1,1) , (2,1) , (3,1) , (4,1) , (5,1) , (6,1)
(1,2) , (2,2) , (3,2) , (4,2) , (5,2) , (6,2)
(1,3) , (2,3) , (3,3) , (4,3) , (5,3) , (6,3)
(1,4) , (2,4) , (3,4) , (4,4) , (5,4) , (6,4)
(1,5) , (2,5) , (3, 5) , (4,5) , (5,5) , (6,5)
(1,6) , (2,6) , (3,6) , (4,6) , (5,6) , (6,6)
now, total possible outcomes are 36
(i) outcomes = (2+6) , (3+5), (4+4) , (5+3), (6+2)
P(SUM=8) = `5/36`
(ii) outcomes= 0
P(SUM=13) = `0/36 = 0`
(iii) outcomes= (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)
P(SUM<=12) = `36/36 = 1`