To determine which quiz the student should study for, we need to compare the probabilities that the student will correctly guess all answers on each quiz.
Step-by-Step Solution:
1. Calculate the probability for the history quiz:
- The history quiz has 5 true-or-false questions.
- For each true-or-false question, the probability of guessing correctly is 0.5.
- The probability of getting all 5 questions correct by guessing is:
[tex]\[
P(\text{History}) = 0.5^5 = 0.03125
\][/tex]
2. Calculate the probability for the science quiz:
- The science quiz has 3 multiple-choice questions.
- For each multiple-choice question, the probability of guessing correctly is 0.25.
- The probability of getting all 3 questions correct by guessing is:
[tex]\[
P(\text{Science}) = 0.25^3 = 0.015625
\][/tex]
3. Compare the probabilities:
- The probability of guessing all questions correctly on the history quiz is 0.03125.
- The probability of guessing all questions correctly on the science quiz is 0.015625.
4. Decision:
- The student should study for the quiz on which the probability of guessing all questions correctly is lower.
- Since [tex]\(0.015625 < 0.03125\)[/tex], the probability of getting all the questions correct by guessing is lower for the science quiz.
Therefore, the student should study for the science quiz.
Correct Answer:
B. Science, because the probability of getting all questions correct is 0.016, which is lower than for history [tex]\(0.031\)[/tex].
