Question

question 7 of 10
a student has to take two quizzes tomorrow. he has only enough time to study for one of them.

• the history quiz has 5 true-or-false questions.
• the science quiz has 3 multiple-choice questions.

the student calculates the probability that he will get all the questions correct by guessing.
chart with columns: (blank), to get 100% correct:, p(guess is correct); rows: history (answer 5 of 5 correctly., 0.5), science (answer 3 of 3 correctly., 0.25)
the student will study for the quiz on which he is likely to do worse by guessing. which quiz should he study for?
a. history, because he must get more questions correct.
b. science, because the probability of getting all questions correct is 0.016, which is lower than for history (0.031).
c. history, because the probability of getting all questions correct is 0.031, which is lower than for science (0.75).
d. science, because the probability of getting all questions correct is 0.075, which is lower than for history (0.25).

Explanation:

Step1: Calculate History Probability

For each history question, \( P(\text{correct}) = 0.5 \). For 5 independent questions, the probability of all correct is \( (0.5)^5 = \frac{1}{32} \approx 0.03125 \).

Step2: Calculate Science Probability

For each science question, \( P(\text{correct}) = 0.25 \). For 3 independent questions, the probability of all correct is \( (0.25)^3 = \frac{1}{64} \approx 0.015625 \).

Step3: Compare Probabilities

Science's probability (≈0.016) is lower than History's (≈0.031), meaning he does worse on Science by guessing. So he should study for Science.

Answer:

B. Science, because the probability of getting all questions correct is 0.016, which is lower than for history (0.031).