Math Problem Statement

answer

A History Test has 3 multiple choice questions with 4 choices each. What is the probability of guessing all 3 questions right?

Solution

The image you've uploaded presents a probability problem. Let's walk through the questions one by one:

  1. Probability of guessing the first question correct: Since there are 4 choices for each multiple-choice question, the probability of guessing correctly is: Probability=14=0.25 or 25%.\text{Probability} = \frac{1}{4} = 0.25 \text{ or } 25\%. This is already correctly provided in the image.

  2. Probability of guessing the first question wrong: If the probability of guessing correctly is 25%, the probability of guessing wrong is: Probability=10.25=0.75 or 75%.\text{Probability} = 1 - 0.25 = 0.75 \text{ or } 75\%. This is also correctly marked in the image.

  3. 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: Probability=(14)×(14)×(14)=164=0.015625.\text{Probability} = \left( \frac{1}{4} \right) \times \left( \frac{1}{4} \right) \times \left( \frac{1}{4} \right) = \frac{1}{64} = 0.015625. Converting this to a percentage and rounding to three significant digits: Probability=0.015625×100=1.56%.\text{Probability} = 0.015625 \times 100 = 1.56\%.

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:

  1. What is the probability of guessing exactly 2 out of 3 questions correctly?
  2. What is the probability of guessing none of the questions correctly?
  3. How does the probability change if there are 5 answer choices per question?
  4. What is the probability of guessing exactly 1 out of 3 questions right?
  5. 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