Question

use the information to answer the question. to win a game at a carnival, players catch a duck floating in a pool. if the duck has a star on the bottom, the player wins a prize. according to the carnival attendant, 20% of the ducks have stars. which model can be used to simulate a player winning a prize?
a. flip a coin. landing on heads simulates the player winning the prize.

b. flip 2 coins. at least 1 coin landing on heads simulates the player winning the prize.

c. choose a marble at random from a bag containing 10 red and 10 blue marbles. choosing a red marble simulates the player winning the prize.

d. spin a spinner with 5 identical sections colored blue, green, red, purple, and yellow. landing on yellow simulates the player winning the prize.

Explanation:

To determine the correct model, we calculate the probability of winning (20% or 0.2) for each option:

• Option A: Probability of heads in a coin flip is \( \frac{1}{2} = 0.5 \) (50%), not 20%.
• Option B: Probability of at least 1 head in 2 coin flips: Total outcomes = 4 (HH, HT, TH, TT). Favorable outcomes (at least 1 head) = 3. Probability = \( \frac{3}{4} = 0.75 \) (75%), not 20%.
• Option C: Total marbles = 20 (10 red + 10 blue). Probability of red = \( \frac{10}{20} = 0.5 \) (50%), not 20%.
• Option D: Spinner has 5 identical sections. Probability of landing on yellow = \( \frac{1}{5} = 0.2 \) (20%), which matches the 20% chance of winning.

Answer:

D. Spin a spinner with 5 identical sections colored blue, green, red, purple, and yellow. Landing on yellow simulates the player winning the prize.