You are taking a multiple choice test that has 20 questions with 4 possible answers each. You randoming quess each answer. What is the probality of getting 7 questions correct?
Pr(7 right, 13 wrong)= .25^7 * .75^13 * number of ways
the number of ways is 20!/(7!13!)
((20 !) / ((7 !) * (13 !))) * (.25^7) * (.75^13) = 0.112406195
check my thinking.
Bonston high school
To find the probability of getting 7 questions correct on a multiple-choice test, we can use the binomial probability formula. The formula is given by:
P(x) = (nCk) * (p^k) * ((1-p)^(n-k))
Where:
P(x) is the probability of getting exactly x questions correct,
n is the total number of trials (number of questions),
k is the number of successful trials (number of correct answers),
p is the probability of success on a single trial (probability of guessing the correct answer),
(1-p) is the probability of failure on a single trial (probability of guessing the wrong answer),
nCk represents the number of ways to choose k successes from n trials.
In this case, n = 20 (number of questions), k = 7 (number of correct answers), p = 1/4 (probability of guessing the correct answer), and (1-p) = 3/4 (probability of guessing the wrong answer).
Therefore, the probability of getting 7 questions correct can be calculated as follows:
P(7) = (20C7) * ((1/4)^7) * ((3/4)^(20-7))
To calculate (20C7), we can use the combination formula:
nCk = n! / (k!(n-k)!),
where ! represents the factorial function.
(20C7) = 20! / (7!(20-7)!) = 77520.
Substituting the values into the formula:
P(7) = 77520 * ((1/4)^7) * ((3/4)^(13))
Calculating the probability:
P(7) ≈ 0.0521
Therefore, the approximate probability of getting 7 questions correct by random guessing is 0.0521 or 5.21%.