Final answer:
In this scenario, a student is taking three quizzes, each out of 3 marks, and the order in which the quizzes are taken doesn't matter. To calculate the probability of a specific outcome, such as scoring a total of 5 marks, we need to determine how many ways we can achieve this outcome and divide it by the total number of possible outcomes. The probability of scoring a total of 5 marks is 1/9 or approximately 0.111.
Step-by-step explanation:
In this scenario, a student is taking three quizzes, each out of 3 marks, and the order in which the quizzes are taken doesn't matter. It only matters what their results are. To calculate the total number of possible outcomes, we can use combinations. Since there are three quizzes and each quiz can have three possible scores (0, 1, or 2), we have 3 options for each quiz. So the total number of possible outcomes is 3 * 3 * 3 = 27.
Now, to find the probability of a specific outcome, such as scoring a total of 5 marks, we need to determine how many ways we can achieve this outcome. We can have (2, 2, 1), (2, 1, 2), or (1, 2, 2) as the scores for the quizzes. So the number of ways to achieve a total of 5 marks is 3.
The probability of scoring a total of 5 marks is the number of ways to achieve 5 marks divided by the total number of possible outcomes: 3/27 = 1/9 or approximately 0.111.