What is the probability of passing a 10-item multiple choice quiz, if there are 4 choices, A to D for every question, and if the passing mark is 8/10, assuming that you guessed the answers to all the questions?
Could somebody help me lol
Well, let's see. Since there are 4 choices for each question, the probability of getting a question right by guessing is 1 out of 4, or 1/4. So, the probability of guessing one question right is 1/4. Since there are 10 questions, the probability of guessing all of them right is (1/4)^10, which is a pretty tiny number.
But hey, don't let that discourage you! Anything is possible, right? Just remember, your chances of passing this quiz by guessing are about as likely as finding a unicorn riding a rainbow while carrying a pot of gold. Good luck!
To find the probability of passing the quiz by guessing, we need to determine the number of ways to answer 8 or more questions correctly out of 10.
Since there are 4 choices for every question, the probability of guessing a single question correctly is 1/4.
Now let's calculate the probability of getting exactly 8, 9, or 10 correct answers.
To get exactly 8 correct answers, you have to choose 8 questions out of the 10 to answer correctly. The remaining 2 questions will be incorrect. The total number of ways to choose 8 questions out of 10 is given by the binomial combination formula, which is:
C(n, k) = n! / (k! * (n-k)!)
Where n is the total number of questions (10) and k is the number of questions answered correctly (8).
So, the number of ways to get exactly 8 correct answers is:
C(10, 8) = 10! / (8! * (10-8)!) = 45
Therefore, the probability of getting exactly 8 correct answers is:
P(8 correct) = (1/4)^8 * (3/4)^2 * 45 = 0.0439
Following the same process, we can calculate the probabilities of getting exactly 9 and 10 correct answers:
P(9 correct) = (1/4)^9 * (3/4)^1 * 10 = 0.0098
P(10 correct) = (1/4)^10 * (3/4)^0 * 1 = 0.0002
Now, the probability of passing the quiz (getting 8, 9, or 10 correct answers) is the sum of these probabilities:
P(passing) = P(8 correct) + P(9 correct) + P(10 correct)
= 0.0439 + 0.0098 + 0.0002
= 0.0539
Therefore, the probability of passing the quiz by guessing is approximately 0.0539, or 5.39%.
prob(right) = 1/4
prob(wrong) = 3/4
if passing grade is 8/10, then I will pass if I get
8/10 or 9/10 or 10/10
prob of that
= C(10,8)(1/4)^8 (3/4)^2 + C(10,9)(1/4)^9 (3/4) + (1/4)^10
= appr .00041
check my arithmetic