Question

each question in a trivia game has 4 answer choices. only 1 answer is correct. which model could be used to simulate a player choosing the correct answer by random? a. flip a coin. landing on heads simulates a player choosing the correct answer by random. b. flip two coins. both coins landing on heads simulates a player choosing the correct answer by random. c. spin a spinner with 8 equal sections labeled 1 to 8. landing on 8 simulates a player choosing the correct answer by random. d. roll a six - sided number cube with sides labeled 1 to 6. rolling an even number simulates a player choosing the correct answer by random.

Explanation:

Step1: Analyze the probability of each option

• Option A: Flip a coin. The probability of landing on heads is \(P(\text{heads})=\frac{1}{2}\), but we need a probability of \(\frac{1}{4}\) (since there are 4 answer choices).
• Option B: Flip two coins. The total number of outcomes is \(n = 2\times2=4\) (HH, HT, TH, TT). The probability of landing on heads - heads is \(P(\text{HH})=\frac{1}{4}\), which simulates a player choosing the correct answer (1 correct out of 4) randomly.
• Option C: Spin a spinner with 8 equal sections. The probability of landing on 8 is \(P(8)=\frac{1}{8}

eq\frac{1}{4}\).

• Option D: Roll a six - sided number cube. The probability of rolling an even number (2, 4, 6) is \(P(\text{even})=\frac{3}{6}=\frac{1}{2}

eq\frac{1}{4}\).

Answer:

B. Flip two coins. Both coins landing on heads simulates a player choosing the correct answer by random.