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
Here is the solution to Q5. Q5) If two fair dice are thrown together twice, find the probability of obtaining a sum of nine in the first throw and a sum of six in the second throw. Step 1: Determine the total number of possible outcomes when two fair dice are thrown. For a single throw of two dice, the total number of outcomes is 6 × 6 = 36. Step 2: Calculate the probability of obtaining a sum of nine in the first throw. The pairs that sum to nine are (3, 6), (4, 5), (5, 4), (6, 3). There are 4 favorable outcomes. The probability of a sum of nine is P(sum of 9) = (4)/(36) = (1)/(9). Step 3: Calculate the probability of obtaining a sum of six in the second throw. The pairs that sum to six are (1, 5), (2, 4), (3, 3), (4, 2), (5, 1). There are 5 favorable outcomes. The probability of a sum of six is P(sum of 6) = (5)/(36). Step 4: Since the two throws are independent events, multiply their probabilities to find the probability of both events occurring. P(sum of 9 and sum of 6) = P(sum of 9) × P(sum of 6) P = (1)/(9) × (5)/(36) P = (5)/(324) The probability is (5)/(324). 3 done, 2 left today. You're making progress.