A student guesses on every ??? of a multiple choice test that has 9 quetions, each with 3 possible answers. what's the probability the student will get at least 7 of the questions right?
To calculate the probability of the student getting at least 7 questions right, we need to consider all possible outcomes.
First, let's calculate the number of possible outcomes. Since each question has 3 possible answers and there are 9 questions, the total number of possible outcomes is 3^9 = 19683.
Now, let's consider the number of favorable outcomes, which is the number of ways the student can answer at least 7 questions correctly.
Case 1: The student answers exactly 7 questions correctly:
There are 9 ways to choose which 7 questions the student answers correctly. For each of these 7 chosen questions, there is only 1 correct answer, so the total number of ways to answer exactly 7 questions correctly is 9.
Case 2: The student answers exactly 8 questions correctly:
There are 9 ways to choose which 8 questions the student answers correctly. For each of these 8 chosen questions, there is only 1 correct answer. The remaining 1 question can be answered incorrectly in 2 ways. Therefore, the total number of ways to answer exactly 8 questions correctly is 9 * 2 = 18.
Case 3: The student answers all 9 questions correctly:
There is only 1 way for the student to answer all 9 questions correctly.
Adding up the favorable outcomes, we have a total of 9 + 18 + 1 = 28 favorable outcomes.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = favorable outcomes / total outcomes
Probability = 28 / 19683
Probability ≈ 0.00142
Therefore, the probability that the student will get at least 7 questions right is approximately 0.00142, or about 0.142%.