Two fair dice A and B, each with faces numbered 1 to 6, are thrown together. a) Construct a table showing all outcomes. b) List pairs summing to more than 10, and at least 10. c) Find probability sum

12) Two fair dice A and B, each with faces numbered 1 to 6, are thrown together. a) Construct a table showing all the equally likely outcomes. The table below shows the outcomes as (Die A, Die B) and their sum. |c|c|c|c|c|c|c| Die A \ Die B & 1 & 2 & 3 & 4 & 5 & 6 \\ 1 & (1,1)=2 & (1,2)=3 & (1,3)=4 & (1,4)=5 & (1,5)=6 & (1,6)=7 \\ 2 & (2,1)=3 & (2,2)=4 & (2,3)=5 & (2,4)=6 & (2,5)=7 & (2,6)=8 \\ 3 & (3,1)=4 & (3,2)=5 & (3,3)=6 & (3,4)=7 & (3,5)=8 & (3,6)=9 \\ 4 & (4,1)=5 & (4,2)=6 & (4,3)=7 & (4,4)=8 & (4,5)=9 & (4,6)=10 \\ 5 & (5,1)=6 & (5,2)=7 & (5,3)=8 & (5,4)=9 & (5,5)=10 & (5,6)=11 \\ 6 & (6,1)=7 & (6,2)=8 & (6,3)=9 & (6,4)=10 & (6,5)=11 & (6,6)=12 \\ b) From your table list the pair of numbers on the two dice for which the sum is i) More than 10 The sums greater than 10 are 11 and 12. The pairs are: (5,6), (6,5), (6,6) ii) At least 10 The sums at least 10 are 10, 11, and 12. The pairs are: (4,6), (5,5), (6,4), (5,6), (6,5), (6,6) c) Find the probability that the sum of the numbers on the two dice is i) More than 10 Step 1: Identify the number of outcomes where the sum is more than 10. From part b) i), there are 3 such outcomes: (5,6), (6,5), (6,6). Step 2: The total number of possible outcomes is 6 × 6 = 36. Step 3: Calculate the probability. P(sum > 10) = Number of outcomes with sum > 10Total number of outcomes = (3)/(36) = (1)/(12) The probability is (1)/(12). ii) At least 10 Step 1: Identify the number of outcomes where the sum is at least 10. From part b) ii), there are 6 such outcomes: (4,6), (5,5), (6,4), (5,6), (6,5), (6,6). Step 2: The total number of possible outcomes is 36. Step 3: Calculate the probability. P(sum 10) = Number of outcomes with sum 10Total number of outcomes = (6)/(36) = (1)/(6) The probability is (1)/(6). What's next?