What is the chance of getting 50/% correct on a test with 20 questions, each question is either True or False. Assume you are blindly guessing and answer all questions
To calculate the chance of getting a certain number of correct answers on a test with multiple-choice questions, we can use the concept of binomial probability. Binomial probability calculates the probability of a specific number of successes (in this case, correct answers) out of a fixed number of trials (the total number of questions on the test).
In this scenario, you are guessing blindly on each question, which means you have a 50% chance of getting each question right. The probability of getting exactly k correct answers out of n questions can be calculated using the binomial probability formula:
P(k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(k) = Probability of getting exactly k correct answers
C(n, k) = The number of combinations of n items taken k at a time (also known as n choose k)
p = Probability of success on a single trial (in this case, the probability of getting a question right, which is 0.5)
n = Total number of trials (the number of questions on the test)
Applying this formula to your scenario, where you have 20 questions on the test and each question has a 50% chance of being answered correctly, we can calculate the probability of getting exactly 50% correct:
P(k=10) = C(20, 10) * 0.5^10 * (1-0.5)^(20-10)
Now, let's calculate it step by step:
C(20, 10) = 20! / (10! * (20-10)!) = 184,756
0.5^10 ≈ 0.0009766
(1-0.5)^(20-10) = 0.5^10 ≈ 0.0009766
P(k=10) = 184,756 * 0.0009766 * 0.0009766 ≈ 0.180
Therefore, the chance of getting exactly 50% correct on a test with 20 True/False questions when guessing blindly is approximately 0.180, or 18.0%.