A student randomly guesses on 10 true or false questions. Use the binomial model to find the probability that the student gets 7 out of the 10 questions right.
A.11.8%
B.20.9%
C.32.4%******
D.50%
The correct answer is A) 11.8% This is a binomial model problem as it is dealing with a situation with only two possible outcomes (incorrect or correct) This means we can use the binomial model formula to calculate a correct answer which in this case we can use the number of trials (questions) of 10 and the number of successes (correct guesses) of 7 with the chance of getting any question correct (which is .500 or 50% because you have a 50/50 chance of guessing any true or false question correctly) and can input all these values into the model formula leading us to our answer of 11.8% I hope this has been of use to you. I wish you all the best in your future study endeavors :)
Yo anyone get the Unit 6 lesson 6 probability models unit test???????
@need a life line...
I have the Probability Unit test I am still working on it and will not just post answers however I am open to solving the problems with you if you need help. text me at (575)-749-9438 or email me gaspervaldi2020 I respond faster to emails than text. I will only be available for this week current date 12/15/2021 end date 12/17/2021
Well, statistically speaking, if a student is randomly guessing on true or false questions, their chances of getting each question right is 50/50. So, let's calculate the probability using the binomial model.
The binomial model formula is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
Where:
- P(x) is the probability of getting x successes
- n is the number of trials (in this case, the number of questions)
- x is the number of successes (in this case, getting 7 questions right)
- p is the probability of success in each trial (in this case, 0.5)
So, plugging in the values:
P(7) = (10C7) * (0.5)^7 * (1-0.5)^(10-7)
Calculating this gives us:
P(7) = (10! / (7!(10-7)!)) * (0.5)^7 * (0.5)^3
Simplifying further:
P(7) = (10! / (7!3!)) * (0.5)^10
Now, let's do some math:
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362880
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
3! = 3 * 2 * 1 = 6
Substituting these values back into the formula:
P(7) = (362880 / (5040 * 6)) * (0.5)^10
P(7) = 0.1171875
So, using the binomial model, the probability that the student gets 7 out of 10 questions right is approximately 0.1171875, which is equivalent to 11.72%. So, none of the options given match this result. Should I try again?
To answer this question using the binomial model, we need two pieces of information: the number of trials (in this case, the number of questions, which is 10) and the probability of success (getting a question right, which is 0.5 since the student is randomly guessing true or false).
The probability of getting exactly 7 out of 10 questions right can be calculated using the binomial probability formula:
P(X = k) = (n C k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes
- n C k is the number of ways of choosing k successes from n trials
- p is the probability of success on a single trial
- (1-p) is the probability of failure on a single trial
In this case, k = 7, n = 10, and p = 0.5. Plugging these values into the formula, we can calculate the probability:
P(X = 7) = (10 C 7) * 0.5^7 * (1-0.5)^(10-7)
Calculating (10 C 7):
(10 C 7) = 10! / (7! * (10-7)!) = 10! / (7! * 3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Plugging these values into the formula:
P(X = 7) = 120 * 0.5^7 * 0.5^3 = 120 * 0.0078125 * 0.125 = 0.9375
So, the probability that the student gets exactly 7 out of 10 questions right is 0.9375 or 93.75%.
None of the given answer options match with the calculated probability. Please double-check the options or re-evaluate the calculation.