you take a three-question multiple-choice test.each question has four choices.you don't know any of the answers. what is the experimental probability that you will guess exactly two out of three correctly

Question

you take a three-question multiple-choice test.each question has four choices.you don't know any of the answers. what is the experimental probability that you will guess exactly two out of three correctly

please help me i am confused

Answer 1

that should have said:

each of the above has a prob of 1/4 x 1/4 x 3/4 = 3/64

so the prob of getting 2 out of 3 correct is 3(3/64) = 9/64

Answer 2

To find the experimental probability of guessing exactly two out of three questions correctly, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Let's break it down step-by-step:

Step 1: Determine the number of possible outcomes
Since each question has four choices, there are a total of 4 possible answers for each question. Therefore, the total number of possible outcomes for all three questions is 4 x 4 x 4 = 64.

Step 2: Determine the number of favorable outcomes
To guess exactly two questions correctly, we need to determine the number of ways we can choose two correct answers out of three questions. This can be calculated using the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of questions and r is the number of questions answered correctly.

In this case, n = 3 (the total number of questions) and r = 2 (the number of questions guessed correctly). Therefore, the number of favorable outcomes is C(3, 2) = 3! / (2!(3-2)!) = 3.

Step 3: Calculate the experimental probability
The experimental probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.

experimental probability = number of favorable outcomes / total number of possible outcomes
experimental probability = 3 / 64

So, the experimental probability of guessing exactly two out of three questions correctly is 3/64, which is approximately 0.0469 or 4.69%.

Answer 3

To calculate the experimental probability of guessing exactly two out of three questions correctly, you need to understand how many different ways you could guess two questions correctly out of three.

Since each question has four choices and you need to guess two correctly, you can choose the two questions you guess correctly in (3 choose 2) = 3 different ways.

For each of these ways, there is a probability of 1/4 for guessing a question correctly and a probability of 3/4 for guessing a question incorrectly. Therefore, the probability of guessing two questions correctly and one question incorrectly is (1/4)^2 * (3/4) = 3/64.

Since there are three different ways to guess two questions correctly out of three, the overall experimental probability is 3 * (3/64) = 9/64.

So, the experimental probability that you will guess exactly two out of three questions correctly is 9/64.

Answer 4

right = r

wrong = w

so you want
rrw
rwr
wrr
each of the above has a prob of 1/4 x 1/4 x 3/4 = 3/16

so the prob of getting 2 out of 3 correct is 3(3/16) = 9/16