You have a 5-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 three out of five questions correctly?
No idea. Take the test a few times and see how many of those times you get 3/5 correct.
.0390625
To find the experimental probability of guessing exactly three out of five questions correctly, we need to understand the total number of possible outcomes or guesses.
For each question, there are four possible choices. Therefore, the total number of possible guesses for one question is 4. Since there are five questions in total, the total number of possible guesses for the entire test is 4^5 (four to the power of five), which equals 1024.
To determine the number of ways in which we can guess exactly three out of five questions correctly, we need to consider different combinations. We can think of this as selecting three questions out of five to guess correctly and multiplying it by the number of possibilities for each correct guess (which is 1) and the number of possibilities for each incorrect guess (which is 3).
Using the concept of combinations, we can calculate the number of ways to choose three questions out of five as "5 choose 3," which is denoted as C(5,3) or 5C3. It can be computed as follows:
C(5,3) = 5! / ((5-3)! * 3!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / 2
= 10
Therefore, the number of ways to guess exactly three out of five questions correctly is 10.
Now, to find the experimental probability, we divide the number of successful outcomes (guessing exactly three out of five questions correctly) by the total number of possible outcomes (1024).
Experimental Probability = Number of successful outcomes / Total number of possible outcomes
= 10 / 1024
≈ 0.00977
So, the experimental probability of guessing exactly three out of five questions correctly is approximately 0.00977, or about 0.977%.