Problem: A six-sided die is thrown once. Find the probability of getting a number which is a multiple of 3.

Here are the solutions to your probability questions: 1. Problem: A six-sided die is thrown once. Find the probability of getting a number which is a multiple of 3. Step 1: Identify the total possible outcomes when rolling a six-sided die. The sample space is \1, 2, 3, 4, 5, 6\. Total number of outcomes = 6. Step 2: Identify the favorable outcomes (multiples of 3). The multiples of 3 in the sample space are \3, 6\. Number of favorable outcomes = 2. Step 3: Calculate the probability. P(multiple of 3) = Number of favorable outcomesTotal number of outcomes = (2)/(6) = (1)/(3) The probability of getting a multiple of 3 is (1)/(3). 2. Problem: A fair die is rolled once. Find the probability of a 4 showing up. Step 1: Identify the total possible outcomes when rolling a fair die. The sample space is \1, 2, 3, 4, 5, 6\. Total number of outcomes = 6. Step 2: Identify the favorable outcome (a 4 showing up). The favorable outcome is \4\. Number of favorable outcomes = 1. Step 3: Calculate the probability. P(4 showing up) = Number of favorable outcomesTotal number of outcomes = (1)/(6) The probability of a 4 showing up is (1)/(6). 3. Problem: A letter is chosen at random from the letters of the word "EXCELLENT". What is the probability that the letter "E" is chosen? Step 1: Count the total number of letters in the word "EXCELLENT". The letters are E, X, C, E, L, L, E, N, T. Total number of letters = 9. Step 2: Count the number of times the letter "E" appears. The letter "E" appears 3 times. Number of favorable outcomes = 3. Step 3: Calculate the probability. P(choosing E) = Number of E'sTotal number of letters = (3)/(9) = (1)/(3) The probability that the letter "E" is chosen is (1)/(3). 4. Problem: In a bag there are 4 blue marbles, 3 red marbles and 2 white marbles. What is the probability of picking at random a red marble? Step 1: Calculate the total number of marbles in the bag. Total marbles = 4 (blue) + 3 (red) + 2 (white) = 9 marbles. Step 2: Identify the number of red marbles. Number of red marbles = 3. Step 3: Calculate the probability of picking a red marble. P(picking a red marble) = Number of red marblesTotal number of marbles = (3)/(9) = (1)/(3) The probability of picking a red marble is (1)/(3). 5. Problem: The probability that a boy will be late for school on any particular day is x. Find, in terms of x, the probability that he will not be late for school. Step 1: Understand the relationship between an event and its complement. The probability of an event happening plus the probability of it not happening is equal to 1. P(event) + P(not event) = 1. Step 2: Apply this to the given problem. Let P(late) be the probability that the boy is late, which is given as x. Let P(not late) be the probability that the boy is not late. P(not late) = 1 - P(late) P(not late) = 1 - x The probability that he will not be late for school is 1 - x. 6. Problem: The probability of Kasukulu waking up late is 0.3. What is the probability that she will wake up early? Step 1: Assume that "waking up early" is the complement of "waking up late". The sum of the probabilities of these two events must be 1. P(late) + P(early) = 1. Step 2: Use the given probability to find the unknown probability. Given P(late) = 0.3. P(early) = 1 - P(late) P(early) = 1 - 0.3 P(early) = 0.7 The probability that she will wake up early is 0.7.