An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. What is the probability that the sum of the dots is divisible by 3?

Answer 1

P(2)=P(12) = 1/36

P(3)=P(11)= 2/36

P(4) = P(10) = 3/36

P(5) =P(9) = 4/36

P(6) =P(8) = 5/36

P(7) = 6/36

P(12)+P(3)+P(9)+P(6) = 1/36+2/36 +4/36+5/36 = 12/36 =1/3 =about 33.3%

P(sum divisible by 3) =

P(1)P(2)+ P(2)P(1)= 2/36

+P(1)P(5)+ P(5)P(1) = 2/36

+P(2)P(4) + P(4)P(2) = 2/36

+P(3)P(3) = 1/36

+P(3)P(6) + P(6)P(3) = 2/36

+P(4)P(5)+ P(5)P(4) = 2/36

+P(6)P(6) = 1/36

=12/36 = 1/3 = about 33.3%