Final answer:
The probability of passing the test with at least 70% is calculated by finding the cumulative probability of getting 7, 8, 9, or 10 questions correct out of 10. Each question can have two outcomes: correct or incorrect. The probability of passing is 0.171875.
Step-by-step explanation:
The probability of passing the test is found by finding the probability of getting at least 70% correct on a 10-question, true-false quiz. Since the student is guessing randomly, there are two possible outcomes for each question: correct (C) or incorrect (I).
The probability of getting a question correct is 0.5, and the probability of getting a question incorrect is 0.5. To calculate the probability of passing with at least 70%, we need to find the cumulative probability of getting 7, 8, 9, or 10 questions correct out of 10.
Step-by-step solution:
1. Find the probability of getting 7 questions correct: P(7 correct) = C(10, 7) * (0.5)^7 * (0.5)^(10-7) = 10 * (0.5)^7 * (0.5)^3 = 0.1171875
2. Find the probability of getting 8 questions correct: P(8 correct) = C(10, 8) * (0.5)^8 * (0.5)^(10-8) = 45 * (0.5)^8 * (0.5)^2 = 0.0439453125
3. Find the probability of getting 9 questions correct: P(9 correct) = C(10, 9) * (0.5)^9 * (0.5)^(10-9) = 10 * (0.5)^9 * (0.5)^1 = 0.009765625
4. Find the probability of getting 10 questions correct: P(10 correct) = C(10, 10) * (0.5)^10 * (0.5)^(10-10) = 1 * (0.5)^10 * (0.5)^0 = 0.0009765625
5. Calculate the cumulative probability of passing with at least 70%: P(passing at least 70%) = P(7 correct) + P(8 correct) + P(9 correct) + P(10 correct)
P(passing at least 70%) = 0.1171875 + 0.0439453125 + 0.009765625 + 0.0009765625 = 0.171875
Your complete question is: A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place four balls (marked A,B,C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are five multiple-choice questions on the exam. What is the probability that she will get
A. five quesions correct?
B. At least four questions correct?
C. No questions correct?
d. No more than two questions correct?