A quiz consists of 10 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 70 %.
I'm not sure what to do. I figured that there's 10 questions, each with a 1/4 chance. I took 10*1/4=2.5 and multiplied that by .70, but my answer wasn't right. What am I missing?
its not even right you chode
You're about 11 years too late Noah
bruh
To find the probability of passing the quiz, we need to consider the minimum passing grade of 70%.
Randomly guessing the answers means that for each question, there is a 1/4 or 0.25 chance of selecting the correct answer and a 3/4 or 0.75 chance of selecting an incorrect answer.
In order to find the probability of passing, we can calculate the probability of failing and subtract it from 1.
To fail the quiz, the student must answer 7 or fewer questions correctly. Let's break it down step by step:
1. Calculate the probability of correctly answering a single question: 1/4 = 0.25
2. Calculate the probability of incorrectly answering a single question: 3/4 = 0.75
3. Calculate the number of ways to answer 0, 1, 2, 3, 4, 5, 6, or 7 questions correctly: C(10,0), C(10,1), C(10,2), ..., C(10,7)
- C(n,r) represents the number of ways to choose r items from a set of n items. It can be calculated using the formula: C(n,r) = n! / (r!(n-r)!)
4. Calculate the probability of answering each of these combinations of questions correctly: (0.25)^k * (0.75)^(10-k) where k represents the number of questions answered correctly.
5. Sum up the individual probabilities for each combination of questions: P(0 correct) + P(1 correct) + P(2 correct) + ... + P(7 correct)
6. Subtract the sum from 1 to get the probability of passing: 1 - P(failure)
This may seem a bit complicated, but luckily, calculators or statistical software can help simplify the calculations.
To pass he must guess
1. exactly 7 out 10 or
2. exactly 8 out 10 or
3. exactly 9out 10 or
4. exactly 10 out 10
prob of exactly 7 out 10 = C(10,7)(1/4)^7(3/4)3 = 120(1/16384)(27/64) = .00309
prob of exactly 8 out 10 = C(10,8)(1/4)^8(3/4)^2 = .000386
prob of exactly 9 out 10 = C(10,9)(1/4)^9(3/4) = .000018
prob of exactly 10 out 10 = C(10,10)(1/4)^10 = .00000095
for a total of .0035055 as the probability.
suggestion: study, and don't guess