test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions.
What is the probability of getting exactly 7 questions correct on this test?
Google "binomial distribution" maybe
To calculate the probability of correctly guessing exactly 7 out of 10 questions, we can use the binomial probability formula.
The binomial formula is given by:
P(X=k) = C(n, k) * p^k * q^(n-k)
Where:
P(X=k) is the probability of getting exactly k successes,
n is the total number of trials (number of questions in this case),
k is the number of desired successes (exactly 7 in this case),
p is the probability of success on an individual trial (1/5, since there are 5 choices for each question),
q is the probability of failure on an individual trial (4/5, since there are 4 incorrect choices for each question),
and C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k!(n-k)!)
Using these values, we can calculate the probability as follows:
P(X=7) = C(10, 7) * (1/5)^7 * (4/5)^(10-7)
C(10, 7) = 10! / (7!(10-7)!) = 10! / (7! * 3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
P(X=7) = 120 * (1/5)^7 * (4/5)^3
Calculating the values:
P(X=7) = 120 * (1/78125) * (64/125) = 120 * (64/78125) * (1/5) = 15360 / 390625 = 0.0394
Therefore, the probability of guessing exactly 7 questions correctly on this test is approximately 0.0394 or 3.94%.
To find the probability of getting exactly 7 questions correct on this test, we need to use the binomial probability formula.
The binomial probability formula is given by:
P(x) = C(n, x) * p^x * (1-p)^(n-x)
Where:
P(x) is the probability of getting exactly x questions correct
C(n, x) is the number of combinations of n items taken x at a time
p is the probability of getting any single question correct
n is the total number of questions
In this case, we have:
- n = 10 (total number of questions)
- x = 7 (number of questions answered correctly)
- p = 1/5 (probability of getting any single question correct by guessing)
First, let's calculate the number of combinations:
C(10, 7) = 10! / (7! * (10-7)!) = 120
Next, let's calculate the probability of getting exactly 7 questions correct:
P(7) = C(10, 7) * (1/5)^7 * (4/5)^(10-7)
P(7) = 120 * (1/5)^7 * (4/5)^3
Calculating this expression gives us the probability of getting exactly 7 questions correct.
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