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
I will read that as you want to get exactly 50% correct, if you mean at least 50% then it would be a long tedious calculation.
prob of (10 of 20 correct)
= C(20,10) (1/2)^10 (1/2)^10
= 184756 ( 1/2^20)
= appr .1762
adf
To find the probability of getting a certain percentage of questions correct on a multiple-choice test with two options (True or False), using blind guesses, we can use the binomial probability formula.
The binomial probability formula is given by:
P(x) = (nCx) * p^x * q^(n-x)
Where:
P(x) is the probability of getting exactly x questions correct,
n is the total number of questions (20 in this case),
x is the number of questions answered correctly,
p is the probability of guessing correctly on a single question (1/2 or 0.5 in this case since there are only two options),
q is the probability of guessing incorrectly on a single question (also 1/2 or 0.5 in this case).
To find the probability of getting exactly 50% correct (10 questions), we can substitute these values into the formula:
P(10) = (20C10) * (0.5)^10 * (0.5)^(20-10)
Now, let's calculate this step by step:
Step 1: Calculate the combination (20C10) or "20 choose 10", which represents the number of ways we can choose 10 questions out of 20.
20C10 = (20!)/(10!(20-10)!) = 184,756
Step 2: Calculate the probability of guessing correctly on 10 questions.
p^x = 0.5^10 = 0.0009765625
Step 3: Calculate the probability of guessing incorrectly on the remaining 10 questions.
q^(n-x) = 0.5^10 = 0.0009765625
Step 4: Multiply all the values together to get the final probability.
P(10) = 184,756 * (0.0009765625) * (0.0009765625) ≈ 0.18055820465
Therefore, the probability of getting exactly 50% correct on the test with blind guesses is approximately 0.1806 or 18.06%.