Two dice are rolled. List all possible Sample spaces. Taka adding of each possiblities which are get the highest odd?

Here are the solutions to your questions: 1) Two dice are rolled. List all possible sample spaces. When adding up each possibility, which one got the highest total? Step 1: List all possible sample spaces when two dice are rolled. Each die has 6 faces (1, 2, 3, 4, 5, 6). When two dice are rolled, the sample space S consists of all ordered pairs (d_1, d_2), where d_1 is the result of the first die and d_2 is the result of the second die. S = (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) There are 6 × 6 = 36 possible outcomes in the sample space. Step 2: Determine which possibility got the highest total when adding up each possibility. The total for each possibility is the sum of the numbers on the two dice (d_1 + d_2). The minimum sum is 1+1=2. The maximum sum is 6+6=12. The possibility that yields the highest total is when both dice show the highest possible number. The highest total is obtained from the outcome (6,6), which sums to 6+6=12. The possibility with the highest total is (6,6). 2) If three dice are tossed, what is the probability of obtaining an even number on all three? Step 1: Determine the total number of possible outcomes. Each die has 6 possible outcomes (1, 2, 3, 4, 5, 6). For three dice, the total number of possible outcomes is 6 × 6 × 6. Total outcomes = 6^3 = 216 Step 2: Determine the number of favorable outcomes (even number on all three dice). For a single die, the even numbers are 2, 4, 6. There are 3 even outcomes. For three dice to show an even number on all three, each die must land on an even number. Favorable outcomes = 3 × 3 × 3 = 27 Step 3: Calculate the probability. The probability of an event is given by the ratio of favorable outcomes to the total number of possible outcomes. P(all three even) = Favorable outcomesTotal outcomes = (27)/(216) Step 4: Simplify the probability. P(all three even) = (27)/(216) = (1)/(8) The probability of obtaining an even number on all three dice is (1)/(8). Send me the next one 📸