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
First, let's list the possible outcomes when a die is rolled and a coin is tossed. The die has 6 outcomes: \1, 2, 3, 4, 5, 6\. The coin has 2 outcomes: \Head (H), Tail (T)\. The total number of possible combined outcomes is 6 × 2 = 12. The sample space is: \(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)\ Step 1: Find the probability of an even number and a head. The even numbers on a die are \2, 4, 6\. The favorable outcomes for an even number and a head are \(2, H), (4, H), (6, H)\. There are 3 favorable outcomes. The probability is the number of favorable outcomes divided by the total number of outcomes. P(even number and head) = Number of favorable outcomesTotal number of outcomes = (3)/(12) = (1)/(4) The probability of an even number and a head is (1)/(4). Step 2: Find the probability of an odd number and a tail. The odd numbers on a die are \1, 3, 5\. The favorable outcomes for an odd number and a tail are \(1, T), (3, T), (5, T)\. There are 3 favorable outcomes. P(odd number and tail) = Number of favorable outcomesTotal number of outcomes = (3)/(12) = (1)/(4) The probability of an odd number and a tail is (1)/(4). Step 3: Find the probability of a number greater than 4 and a head. The numbers greater than 4 on a die are \5, 6\. The favorable outcomes for a number greater than 4 and a head are \(5, H), (6, H)\. There are 2 favorable outcomes. P(number greater than 4 and head) = Number of favorable outcomesTotal number of outcomes = (2)/(12) = (1)/(6) The probability of a number greater than 4 and a head is (1)/(6). Send me the next one 📸