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
let's solve this die problem. When a fair die is tossed once, the sample space (all possible outcomes) is: S = \1, 2, 3, 4, 5, 6\ The total number of possible outcomes is n(S) = 6. a) obtaining the number 5 Step 1: Count the number of times '5' appears in the sample space. The number 5 appears 1 time. Step 2: Calculate the probability. P(obtaining 5) = Number of times 5 appearsTotal number of outcomes = (1)/(6) The probability of obtaining the number 5 is (1)/(6). b) obtaining the number 8 Step 1: Count the number of times '8' appears in the sample space. The number 8 does not appear on a standard fair die. So, it appears 0 times. Step 2: Calculate the probability. P(obtaining 8) = Number of times 8 appearsTotal number of outcomes = (0)/(6) = 0 The probability of obtaining the number 8 is 0. c) obtaining an even number Step 1: Identify and count the even numbers in the sample space. The even numbers are 2, 4, 6. There are 3 even numbers. Step 2: Calculate the probability. P(obtaining an even number) = Number of even numbersTotal number of outcomes = (3)/(6) = (1)/(2) The probability of obtaining an even number is (1)/(2). d) obtaining an odd number Step 1: Identify and count the odd numbers in the sample space. The odd numbers are 1, 3, 5. There are 3 odd numbers. Step 2: Calculate the probability. P(obtaining an odd number) = Number of odd numbersTotal number of outcomes = (3)/(6) = (1)/(2) The probability of obtaining an odd number is (1)/(2). What's next?