A multiple choice test has 20 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.
1) What is the probability of getting exactly 9 correct answers?
2)What is the probability of getting less than 9 correct answers?
prob of R(ight) = 4/20 = 1/5
prob of W(rong) = 4/5
1) to have exactly 9R and 11W
= C(20,9)((1/5)^9(4/5)^11
= ....
( I got .00722)
2) to get the prob of less than 9 you will have to do
prob(0R) + prob(1R) + prob(2R) + .. + prob(8R)
I will do prob(R4)
= C(20,4)(1/4)^4(4/5)^16 = .21819
Follow the same pattern for the other calculations
a test consists of 25 multiple choice questions. Each has 5 possible answers, which only one is correct. If a student guesses on each question, find the following:
a) prob that he will guess all of them right
b)prob that he will guess at most 12 right
c) prob that he will guess at least 1 right
d) mean and stndrd. deviation of the number of correct answers
e)estimate the prob of the number of correct answers that will fall within the limits -----> miu +or- 2(stand.dev)
Suppose a student takes a 20 question multiple-choice test and guesses at every answer. If there are exactly four choices on each question, what is the probability the student passes the test? (Assume passing means the student gets at least 60% of the questions correct.)
Well, isn't multiple choice just a fancy name for "guessing game"? Let's dive into it!
1) The probability of getting exactly 9 correct answers is like finding a unicorn in a haystack. It's a bit of a long shot. To calculate the probability, we need to use the binomial probability formula. The probability of getting exactly 9 correct answers out of 20 questions is approximately 0.073. So, it's as likely as finding a needle in a haystack made of marshmallows!
2) Now, let's talk about the probability of getting less than 9 correct answers. Well, there are two possibilities: either you get 8 correct or fewer. Since we don't want to do the math, let's just say the probability is higher than the number of times your stomach growled during a boring lecture. If I were to hazard a guess, I'd say it's around 0.093. So, you have slightly better chances of getting less than 9 correct answers than the chances of me becoming a lion tamer.
To find the probability of a specific outcome or event, we can use the concept of probability and the formula for calculating the probability of an event in a sample space.
1) To find the probability of getting exactly 9 correct answers, we need to calculate the probability for each individual question and then multiply them together.
Each question has 4 possible answers, with only one being correct. Therefore, the probability of guessing the correct answer to a single question is 1/4. Similarly, the probability of guessing the incorrect answer to a single question is 3/4.
To find the probability of getting exactly 9 correct answers, we need to calculate the probability of getting 9 correct and 11 incorrect answers out of 20 questions. This can be done using the binomial probability formula:
P(X=k) = (nCk) * (p^k) * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k correct answers,
- n is the total number of trials (20 questions in this case),
- k is the number of successful outcomes (9 correct answers in this case),
- p is the probability of success in a single trial (1/4 in this case).
Plugging in the values, we have:
P(X=9) = (20C9) * ((1/4)^9) * ((3/4)^(20-9))
Now, we can calculate this probability:
P(X=9) = (20C9) * (1/4)^9 * (3/4)^11
Calculating (20C9) can be done using the combination formula:
(20C9) = 20! / (9! * (20-9)!)
Plugging this value into the probability formula, we can calculate the probability of getting exactly 9 correct answers.
2) To find the probability of getting less than 9 correct answers, we need to calculate the cumulative probability up to 8 correct answers.
We can calculate the probability of getting 0, 1, 2, ..., 8 correct answers using the same formula mentioned above, and then sum them up.
P(X<9) = P(X=0) + P(X=1) + P(X=2) + ... + P(X=8)
Each of these probabilities can be calculated using the binomial probability formula as explained in the first question.
By summing up the probabilities, we get the probability of getting less than 9 correct answers.