This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Here's how to solve this probability problem. Step 1: Determine the total number of possible outcomes when two fair dice are thrown. When two fair dice are thrown, each die has 6 possible outcomes. The total number of possible outcomes is 6 × 6 = 36. Step 2: Calculate the probability of obtaining a sum of nine in the first throw. The combinations that result in a sum of nine are: (3, 6), (4, 5), (5, 4), (6, 3) There are 4 favorable outcomes for a sum of nine. The probability of getting a sum of nine, P(sum=9), is: P(sum=9) = Number of favorable outcomesTotal number of outcomes = (4)/(36) = (1)/(9) Step 3: Calculate the probability of obtaining a sum of six in the second throw. The combinations that result in a sum of six are: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) There are 5 favorable outcomes for a sum of six. The probability of getting a sum of six, P(sum=6), is: P(sum=6) = Number of favorable outcomesTotal number of outcomes = (5)/(36) Step 4: Calculate the probability of both independent events occurring. Since the two throws are independent events, the probability of both events happening is the product of their individual probabilities: P(sum=9 in 1st throw AND sum=6 in 2nd throw) = P(sum=9) × P(sum=6) P = (1)/(9) × (5)/(36) P = (1 × 5)/(9 × 36) P = (5)/(324) The probability of obtaining a sum of nine in the first throw and a sum of six in the second throw is (5)/(324). Got more? Send 'em.