A multiple

-
choice quiz
contains 5 questions with 4
choices for each answer.
A
student passes the quiz if they get at
least an 80% on the quiz
.
If a student guesses
on every question
, find the probability that
she
passes
the quiz
.
I have tried c(20,8)(1/4)^8(3/4)^12
c(20,9)(1/4)^9(3/4)^11
c(20,10)(1/4)^10(3/4)^11

Well, let me start by saying that you have definitely tried some options there! But let's see if I can help you figure out the correct approach to calculating the probability.

First, let's consider the probability of guessing a single question correctly. Since there are 4 choices for each question and only one correct answer, the probability of guessing the correct answer for any given question is 1/4.

Now, in order to pass the quiz, the student needs to get at least 80% of the questions right. Since there are 5 questions in total, this means they need to get 4 or 5 questions correct.

To calculate the probability of passing the quiz, we need to consider two scenarios:
1. The student guesses exactly 4 questions correctly.
2. The student guesses all 5 questions correctly.

Let's calculate the probability for each scenario:

1. For the student to guess exactly 4 questions correctly, we can use the binomial probability formula. The probability of getting 4 questions right is (20 C 4) * (1/4)^4 * (3/4)^16, where (20 C 4) represents the number of ways to choose 4 questions out of 20.

2. For the student to guess all 5 questions correctly, we can use the same formula. The probability of getting 5 questions right is (20 C 5) * (1/4)^5 * (3/4)^15.

Now, we need to add up the probabilities of both scenarios, since either one will result in the student passing the quiz.

P(passing the quiz) = P(guessing 4 questions correctly) + P(guessing all 5 questions correctly)

You can calculate these probabilities separately and add them up to get the final answer.

Note: The formula you used to calculate the probabilities is close, but it seems like the number of incorrect answers in the formula should be decreased as we need to consider the scenarios where the student guesses more than one question correctly.

I hope this explanation helps you in finding the correct probability. Good luck with your calculations!

To find the probability that the student passes the quiz by guessing on every question, we need to determine the number of ways the student can answer at least 80% of the questions correctly.

The probability of getting a question correct by guessing is 1/4, and the probability of getting a question wrong is 3/4.

Let's break down the different scenarios:

1. Getting exactly 4 questions correct: (1/4)^4 * (3/4)^16 * c(20, 4)
This calculation accounts for the probability of getting exactly 4 questions correct out of 20, and the probability of getting the rest wrong. "c(20, 4)" represents the number of ways to choose 4 questions out of 20 to answer correctly.

2. Getting exactly 5 questions correct: (1/4)^5 * (3/4)^15 * c(20, 5)
This calculation accounts for the probability of getting exactly 5 questions correct out of 20, and the probability of getting the rest wrong. "c(20, 5)" represents the number of ways to choose 5 questions out of 20 to answer correctly.

3. Getting exactly 6 questions correct: (1/4)^6 * (3/4)^14 * c(20, 6)
This calculation accounts for the probability of getting exactly 6 questions correct out of 20, and the probability of getting the rest wrong. "c(20, 6)" represents the number of ways to choose 6 questions out of 20 to answer correctly.

To find the probability of passing the quiz, we add up the probabilities of these different scenarios and divide by the total number of possible outcomes (which is 4^20, since there are 4 choices for each question):

Probability of passing = (probability of scenario 1 + probability of scenario 2 + probability of scenario 3) / (4^20)

I hope this helps! Let me know if you have any further questions.

To find the probability that the student passes the quiz by guessing, we need to calculate the probability of getting at least 80% correct.

Let's break down the calculation step by step:

Step 1: Calculate the probability of getting each individual question correct by guessing. Since there are 4 choices for each question, the probability of guessing the correct answer is 1/4.

Step 2: Determine the number of questions the student needs to get correct in order to pass the quiz. To achieve at least 80%, the student needs to answer 4 out of the 5 questions correctly.

Step 3: Use the binomial probability formula to calculate the probability that the student gets exactly 4 or 5 questions correct. The formula is:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

where:
- P(X=k) is the probability of getting exactly k correct answers
- C(n,k) is the number of ways to choose k correct answers out of n total questions
- p is the probability of getting one question correct (1/4)
- n is the total number of questions (5)
- k is the number of correct answers needed to pass (4 or 5)

Step 4: Calculate the probabilities for each scenario (4 or 5 correct answers) and add them together to get the total probability of passing the quiz.

Here's the correct calculation:

P(pass) = P(X=4) + P(X=5)
= C(5,4) * (1/4)^4 * (3/4)^(5-4) + C(5,5) * (1/4)^5 * (3/4)^(5-5)
= 5 * (1/4)^4 * (3/4)^1 + 1 * (1/4)^5 * (3/4)^0
= 5 * (1/256) * (3/4) + 1 * (1/1024) * 1
= 15/1024 + 1/1024
= 16/1024
= 1/64

Therefore, the probability that the student passes the quiz by guessing is 1/64.