Math Problem Statement
answer
Solution
The image you've uploaded presents a probability problem. Let's walk through the questions one by one:
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Probability of guessing the first question correct: Since there are 4 choices for each multiple-choice question, the probability of guessing correctly is: This is already correctly provided in the image.
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Probability of guessing the first question wrong: If the probability of guessing correctly is 25%, the probability of guessing wrong is: This is also correctly marked in the image.
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Probability of guessing all 3 questions right: Since each question is independent, the probability of guessing all three correctly is the product of the probabilities of guessing each one correctly: Converting this to a percentage and rounding to three significant digits:
Thus, the probability of guessing all three questions correctly is approximately 1.56%.
Would you like more details on how I calculated these probabilities, or do you have further questions? Here are 5 related questions you might find interesting:
- What is the probability of guessing exactly 2 out of 3 questions correctly?
- What is the probability of guessing none of the questions correctly?
- How does the probability change if there are 5 answer choices per question?
- What is the probability of guessing exactly 1 out of 3 questions right?
- What is the expected number of correct answers if you guess randomly for all 3 questions?
Tip: When dealing with independent events, the overall probability is the product of the individual probabilities.
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Math Problem Analysis
Mathematical Concepts
Probability
Independent Events
Formulas
Probability of event A = 1/4
Probability of independent events happening together: P(A and B and C) = P(A) * P(B) * P(C)
Theorems
The multiplication rule of independent events
Suitable Grade Level
Grades 7-9
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