Final answer:
The probability of missing at least one question on a quiz with 5 true/false and 5 multiple-choice questions, when guessing randomly, is approximately 99.997%, corresponding to answer choice C.
Step-by-step explanation:
To calculate the probability of missing at least one question:
- Calculate the probability of getting a question right:
- True/False question: 1/2 chance of guessing correctly.
- Multiple-choice question with 4 choices: 1/4 chance of guessing correctly.
Calculate the probability of guessing all questions right:
- Probability of guessing all true/false questions correctly: (1/2)^5.
- Probability of guessing all multiple-choice questions correctly: (1/4)^5.
- Total probability of guessing all questions correctly: (1/2)^5 * (1/4)^5.
Find the complementary probability of not guessing all questions correctly, which gives us the probability of missing at least one question.
- Complementary probability: 1 - ((1/2)^5 * (1/4)^5).
- Perform the calculation: 1 - (1/32 * 1/1024).
- This equals 1 - (1/32768), which simplifies to 32767/32768.
- Convert to a percentage: (32767/32768) * 100%, roughly 99.997%.
Therefore, the probability of missing at least one question when randomly guessing is approximately 99.997%, which corresponds to answer choice C.