A multiple-choice quiz has 15 questions, each with 4 possible answers of which only 1 is the correct answer. What is the probability that a student gets exactly 8 correct answers?
0.0131
TANG INA NYO MGA BOBO WALANG KWENTA
JOKE HEHE MAY SAGOT PALA SORRY GUYS
To find the probability that a student gets exactly 8 correct answers, we need to evaluate the probability of getting 8 correct answers and 7 incorrect answers and multiply them together.
The probability of getting 8 correct answers can be calculated using the binomial probability formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of getting exactly k successes (in this case, correct answers)
C(n, k) is the number of ways to choose k successes out of n trials (combination formula)
p is the probability of getting a correct answer on any given trial
(1-p) is the probability of getting an incorrect answer on any given trial
n is the total number of trials (in this case, the number of questions)
In this case, we have:
n = 15 (total number of questions)
k = 8 (number of correct answers)
p = 1/4 (probability of getting a correct answer)
Let's calculate the probability:
First, calculate the combination C(n, k):
C(15, 8) = 15! / (8! * (15-8)!)
= (15 * 14 * 13 * 12 * 11 * 10 * 9 * 8!) / (8! * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= (15 * 14 * 13 * 12 * 11 * 10 * 9) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
= 6435
Next, calculate the probability:
P(X=8) = C(15, 8) * (1/4)^8 * (3/4)^(15-8)
P(X=8) = 6435 * (1/4)^8 * (3/4)^7
P(X=8) = 6435 * (1/4)^8 * (3/4)^7
= 0.0916 (rounded to 4 decimal places)
Therefore, the probability that a student gets exactly 8 correct answers is approximately 0.0916 or 9.16%.