You are taking a multiple choice test that has 20 questions with 4 possible answers each. You randoming quess each answer. What is the probality of getting 7 questions correct?

Question

You are taking a multiple choice test that has 20 questions with 4 possible answers each. You randoming quess each answer. What is the probality of getting 7 questions correct?

Answer 1

I do not understand what I need to do here...very confused...would I multiply 20 x 4 to get 80/7?

Answer 2

4 out of 20. talk to me about this.

Answer 3

It's not 4 out of 20

Answer 4

To calculate the probability of getting exactly 7 questions correct by randomly guessing on a multiple-choice test, we need to use the concept of binomial probability.

The probability of getting a specific question correct by random guessing is 1 out of 4, or 1/4. Similarly, the probability of getting a specific question wrong is 3 out of 4, or 3/4.

Since there are 20 questions in total and you are randomly guessing each answer, we can treat each question as an independent event. Thus, to find the probability of getting exactly 7 questions correct, we need to calculate the probability of getting 7 questions correct and 13 questions incorrect, and then multiply them together.

The formula to calculate the binomial probability is:

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

Where:
- P(X=k) is the probability of getting exactly k successes (in this case, 7 questions correct).
- C(n, k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.
- p is the probability of success on a single trial (in this case, 1/4).
- (1-p) is the probability of failure on a single trial (in this case, 3/4).
- n is the total number of trials (in this case, 20 questions).

Using this formula, we can calculate the probability as follows:

P(X=7) = C(20, 7) * (1/4)^7 * (3/4)^(20-7)

Now, let's plug in the values into the formula and calculate the probability:

P(X=7) = C(20, 7) * (1/4)^7 * (3/4)^13

To calculate the binomial coefficient, we use the formula:

C(n, k) = n! / (k! * (n-k)!)

C(20, 7) = 20! / (7! * (20-7)!)

Now, let's calculate the binomial coefficient:

C(20, 7) = (20 * 19 * 18 * 17 * 16 * 15 * 14) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

Using a calculator or a mathematical software, we can compute:

C(20, 7) ≈ 77520

Now, we can calculate the probability:

P(X=7) ≈ 77520 * (1/4)^7 * (3/4)^13

Using a calculator or a spreadsheet, we can find:

P(X=7) ≈ 0.0015507

So the probability of getting exactly 7 questions correct by random guessing in a multiple-choice test with 20 questions is approximately 0.0015507, or about 0.15%.