Let's calculate the probability of the student getting all questions correct by guessing for each quiz.
### History Quiz
- The history quiz consists of 4 true-or-false questions.
- The probability of guessing a true-or-false question correctly is [tex]\( 0.5 \)[/tex].
To calculate the probability of getting all 4 questions correct:
[tex]\[ P_{history} = 0.5^4 \][/tex]
### Calculation for History Quiz:
[tex]\[ P_{history} = 0.5 \times 0.5 \times 0.5 \times 0.5 = 0.5^4 = 0.0625 \][/tex]
So, the probability of the student getting all the history questions correct by guessing is 0.0625.
### Science Quiz
- The science quiz consists of 3 multiple-choice questions.
- The probability of guessing a multiple-choice question correctly is [tex]\( 0.2 \)[/tex].
To calculate the probability of getting all 3 questions correct:
[tex]\[ P_{science} = 0.2^3 \][/tex]
### Calculation for Science Quiz:
[tex]\[ P_{science} = 0.2 \times 0.2 \times 0.2 = 0.2^3 = 0.008 \][/tex]
So, the probability of the student getting all the science questions correct by guessing is 0.008.
### Decision
The student is more likely to get worse on the quiz with the lower probability of getting all the questions correct by guessing.
- Probability of getting all history questions correct: [tex]\( 0.0625 \)[/tex]
- Probability of getting all science questions correct: [tex]\( 0.008 \)[/tex]
Since [tex]\( 0.008 \)[/tex] (science) is less than [tex]\( 0.0625 \)[/tex] (history), the student is more likely to do worse on the science quiz by guessing.
Therefore, the student should study for the Science quiz.
