You have a ten question multiple choice test in your next class and you did not study at all. Each question has four choices and only one correct answer. You are going to guess on each question. What is the probability that you score at least a 20% on the test.
first then we have 40 questions okay well the chance of getting 2 or more questions is at random but due to this being a experimental answer in math we would say the answer is 0.5 the math that Mathmate shows has flaws in it he didnt follow the certain steps but he got the wrong answer only problem i see in there is a few steps in the process but he did do good, i just wish mathmate showed the work better because alot of it is not fully the answer and only the almost full answer and then you cannot show your work the work "p=0.25
n=10
P(r)=number of question correct
=nCr(p^r)(1-p)^(n-r)
nCr = binomial coefficient = n!/((n-r)!r!)
P(0)=0.0563 (zero question correct)
P(1)=0.1877 (1 question correct)" is to advanced for grades lower than 9th so your teacher wont believe that the easiest way to do it is to do the statistics by using 20/40 or 2/4ths and dividing to get the answer of 0.5 or because the way you do it isnt right if you guess have 4 questions for each question then the answer has to be 2/4 and in school even guessing with that many questions the rule is if you guessed even blindfolded then unless your trying to fail then you should get a 20% or higher so hope i helped!
To find the probability of scoring at least a 20% on the test, we need to consider the possible outcomes for each question. Since there are four choices and only one correct answer, the probability of guessing the correct answer for each question is 1/4.
Now, let's analyze the scenario. If you guess on each question, there are two possible outcomes: either you answer correctly, or you answer incorrectly.
To calculate the probability of scoring at least 20%, we need to consider the different combinations of correct and incorrect answers. Let's analyze this step by step:
First, let's find the probability of answering all questions incorrectly. Since each question has a 1/4 probability of guessing correctly, the probability of guessing incorrectly for one question is 3/4. Considering this, the probability of answering all ten questions incorrectly is:
(3/4) * (3/4) * (3/4) * (3/4) * (3/4) * (3/4) * (3/4) * (3/4) * (3/4) * (3/4) = (3/4)^10
Next, since the probability of answering all questions incorrectly is the same as guessing correctly, we can calculate the probability for guessing at least one question correctly by subtracting the probability of answering all questions incorrectly from 1:
1 - (3/4)^10
Calculating this, we find that the probability of guessing at least one question correctly and scoring at least 20% on the test is approximately:
1 - (3/4)^10 ≈ 0.8287 or 82.87%
Therefore, the probability of scoring at least a 20% on the test by guessing on each question is approximately 82.87%.
Use binomial probability because:
probability is known and does not change over the experiment,
outcome is binomial (success or failure),
each step of the experiment is similar,
p=0.25
n=10
P(r)=number of question correct
=nCr(p^r)(1-p)^(n-r)
nCr = binomial coefficient = n!/((n-r)!r!)
P(0)=0.0563 (zero question correct)
P(1)=0.1877 (1 question correct)
Therefore, to get at least 20%, or 2 or more questions correct, we have
P(2+)=1-(P(0)+P(1))
=0.7560