Answer :
To determine which quiz the student should study for, we need to compare the probabilities of guessing all the questions correctly on each quiz.
### History Quiz
- The history quiz consists of 5 true-or-false questions.
- The probability of guessing each question correctly is 0.5.
The probability of guessing all 5 questions correctly (P_history) can be calculated as:
[tex]\[ P_{\text{history}} = 0.5^5 \][/tex]
[tex]\[ P_{\text{history}} = 0.031 \][/tex]
### Science Quiz
- The science quiz consists of 4 multiple-choice questions, where each question has more than two possible answers (assumed to be 1 in 5 or P = 0.2).
- The probability of guessing each question correctly is 0.2.
The probability of guessing all 4 questions correctly (P_science) can be calculated as:
[tex]\[ P_{\text{science}} = 0.2^4 \][/tex]
[tex]\[ P_{\text{science}} = 0.002 \][/tex]
### Comparison
Now that we have the probabilities:
- Probability of getting all history questions correct: [tex]\( P_{\text{history}} = 0.031 \)[/tex]
- Probability of getting all science questions correct: [tex]\( P_{\text{science}} = 0.002 \)[/tex]
The student should study for the quiz on which he has a lower probability of guessing all answers correctly. In this case, the probability of getting all science questions correct (0.002) is lower than the probability of getting all history questions correct (0.031).
Therefore, the student should study for the science quiz, as his chances of getting all answers correct on the science quiz by guessing are lower.
Thus, the correct answer is:
B. Science, because the probability of getting all questions correct is 0.002 , which is lower than for history (0.031).
### History Quiz
- The history quiz consists of 5 true-or-false questions.
- The probability of guessing each question correctly is 0.5.
The probability of guessing all 5 questions correctly (P_history) can be calculated as:
[tex]\[ P_{\text{history}} = 0.5^5 \][/tex]
[tex]\[ P_{\text{history}} = 0.031 \][/tex]
### Science Quiz
- The science quiz consists of 4 multiple-choice questions, where each question has more than two possible answers (assumed to be 1 in 5 or P = 0.2).
- The probability of guessing each question correctly is 0.2.
The probability of guessing all 4 questions correctly (P_science) can be calculated as:
[tex]\[ P_{\text{science}} = 0.2^4 \][/tex]
[tex]\[ P_{\text{science}} = 0.002 \][/tex]
### Comparison
Now that we have the probabilities:
- Probability of getting all history questions correct: [tex]\( P_{\text{history}} = 0.031 \)[/tex]
- Probability of getting all science questions correct: [tex]\( P_{\text{science}} = 0.002 \)[/tex]
The student should study for the quiz on which he has a lower probability of guessing all answers correctly. In this case, the probability of getting all science questions correct (0.002) is lower than the probability of getting all history questions correct (0.031).
Therefore, the student should study for the science quiz, as his chances of getting all answers correct on the science quiz by guessing are lower.
Thus, the correct answer is:
B. Science, because the probability of getting all questions correct is 0.002 , which is lower than for history (0.031).
