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

The chance of getting an item right = 1/4. The chance of getting it wrong = 3/4.

The probability of getting 2 right and one wrong is found by multiplying the individual probabilities.

No problem, I can help you with that! To find the experimental probability of guessing exactly two out of three questions correctly, we first need to understand the total number of possible outcomes.

In this scenario, since each question has four choices, there are four possible answers for each question. Therefore, the total number of possible outcomes can be calculated as 4 × 4 × 4, which equals 64.

Now, let's consider the number of ways you can guess exactly two questions correctly. To determine this, we need to calculate the number of combinations. The formula to find the number of combinations is nCr = n! / (r! * (n - r)!), where n is the total number of options and r is the number of choices.

In this case, we want to find the number of ways to guess exactly 2 out of 3 correctly. So, using the nCr formula, we have:

3C2 = 3! / (2! * (3 - 2)!)
= 3! / (2! * 1!)
= 3 / (2 * 1)
= 3 / 2
= 1.5

Therefore, there are 1.5 ways to guess exactly two questions correctly. However, since we can't have a fraction of ways, we round it down to the nearest whole number, which in this case is 1.

So, the number of ways to guess exactly two out of three questions correctly is 1.

To find the experimental probability, we divide the number of successful outcomes (1) by the total number of possible outcomes (64).

Experimental Probability = Number of successful outcomes / Total number of possible outcomes
= 1 / 64
≈ 0.01563

Therefore, the experimental probability of guessing exactly two out of three questions correctly is approximately 0.01563, or you can also say it is about 1.56%.