This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like on a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability is count of favorable divided by total, such as even on die {2,4,6} count 3, total 6, P=3/6=1/2, and verify probabilities sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. The correct model treats each of the 6 sections equally, with 3 labeled C, so P(C)=3/6. A common error is assigning probability per label instead of per section, like 1/3 for three labels, or treating as one outcome per letter leading to 1/6. To create the model: (1) identify equally likely outcomes (fair spinner sections yes), (2) count n=6, (3) assign each P=1/6, (4) verify sum=1. To calculate the event: (1) identify favorable C sections, (2) count 3, (3) divide by 6, (4) simplify to 1/2 but option is 3/6; mistakes include non-equal probabilities or probability >1.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability is count of favorable divided by total, such as even on die {2,4,6} count 3, total 6, P=3/6=1/2, and verify probabilities sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. Here, the correct model assigns P=1/12 to each ticket 1-12, so P(multiple of 3)={3,6,9,12} which is 4/12. A common error is missing multiples like 12 or using wrong total, leading to incomplete sample space. To create the model: (1) identify equally likely outcomes (identical tickets yes), (2) count n=12, (3) assign each P=1/12, (4) verify sum=1. To calculate: (1) identify favorable multiples of 3, (2) count 4, (3) divide by 12, (4) simplify to 1/3 but 4/12 is equivalent; mistakes include wrong identification or not summing to 1.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability: count favorable, divide by total (even on die: {2,4,6} count 3, total 6, P=3/6=1/2), verify sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. Here, the correct model for MATH has slips {M,A,T,H}, each P=1/4, P(A)=1/4. A common error is treating repeated letters as one or using word length incorrectly like 1/3. To create the model: (1) identify equally likely slips (mixed yes), (2) count n=4, (3) assign each P=1/4, (4) verify sum=1. To calculate the event: (1) identify favorable {A}, (2) count 1, (3) divide by 4, (4) simplify to 1/4; mistakes include assuming non-uniform or wrong total.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like on a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability is count of favorable divided by total, such as even on die {2,4,6} count 3, total 6, P=3/6=1/2, and verify probabilities sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. The correct model here assigns each of the 10 marbles equal probability 1/10, with 3 blue, so P(blue)=3/10. A common error is using only blue and another color, like 3/5 for blue over red, or inverting to 10/3 which exceeds 1. To create the model: (1) identify equally likely outcomes (each marble yes), (2) count n=10, (3) assign each P=1/10, (4) verify sum=1. To calculate the event: (1) identify favorable blue marbles, (2) count 3, (3) divide by 10, (4) leave as 3/10; mistakes include wrong probabilities or incomplete sample space.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like on a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability is count of favorable divided by total, such as even on die {2,4,6} count 3, total 6, P=3/6=1/2, and verify probabilities sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. The correct model here identifies the even numbers as {2,4,6}, so P=3/6=1/2. A common error is miscounting favorable outcomes, like thinking only two evens, leading to 2/6, or confusing probability with counts, resulting in values like 3 or greater than 1. To create the model: (1) identify equally likely outcomes (fair die yes), (2) count n=6, (3) assign each P=1/6, (4) verify sum=1. To calculate the event: (1) identify favorable {2,4,6}, (2) count 3, (3) divide by 6, (4) simplify to 1/2; mistakes include assuming non-uniform without justification or incorrect counting.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability: count favorable, divide by total (even on die: {2,4,6} count 3, total 6, P=3/6=1/2), verify sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. Here, the correct model for the spinner has sample space {1,2,3,4,5,6,7,8}, each with P=1/8, and P(greater than 6) is {7,8} so 2 favorable over 8 total, 2/8. A common error is counting incorrectly like 6/8 for less than or equal to 6, or simplifying wrongly to 2/6. To create the model: (1) identify equally likely sections (fair spinner yes), (2) count n=8, (3) assign each P=1/8, (4) verify sum=1. To calculate the event: (1) identify favorable {7,8}, (2) count 2, (3) divide by 8, (4) simplify to 1/4; mistakes include assuming non-uniform or not summing to 1.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like on a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability is count of favorable divided by total, such as even on die {2,4,6} count 3, total 6, P=3/6=1/2, and verify probabilities sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. The correct model lists the favorable outcomes for greater than 4 as {5,6}. A common error is including 4 in greater than 4, like {4,5,6}, or using less than, like {1,2,3,4}. To create the model: (1) identify equally likely outcomes (fair die yes), (2) count n=6, (3) assign each P=1/6, (4) verify sum=1. To calculate the event: (1) identify favorable >4 as {5,6}, (2) count 2, (3) divide by 6 for probability, but here it's listing the set; mistakes include wrong event definition or incomplete sample space.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like on a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability is count of favorable divided by total, such as even on die {2,4,6} count 3, total 6, P=3/6=1/2, and verify probabilities sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. The correct model has four outcomes {HH,HT,TH,TT}, each P=1/4, with exactly one head as {HT,TH}, so P=2/4=1/2. A common error is counting three for one head, leading to 3/4, or thinking only one outcome like 1/4. To create the model: (1) identify equally likely outcomes (fair coin flips yes), (2) count n=4, (3) assign each P=1/4, (4) verify sum=1. To calculate the event: (1) identify favorable {HT,TH}, (2) count 2, (3) divide by 4, (4) simplify to 1/2; mistakes include incomplete sample space or probabilities >1.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability is count of favorable divided by total, such as even on die {2,4,6} count 3, total 6, P=3/6=1/2, and verify probabilities sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. Here, the correct model assigns P=1/6 to each face, so P(4)=1/6 since one favorable outcome out of six. A common error is miscounting outcomes or assuming non-uniform probabilities, like thinking P(4)=1/5 by excluding 4 incorrectly. To create the model: (1) identify equally likely outcomes (fair die yes), (2) count n=6, (3) assign each P=1/6, (4) verify sum=1. To calculate: (1) identify favorable {4}, (2) count 1, (3) divide by 6, (4) simplify to 1/6; mistakes include wrong total or not verifying sum to 1.

This question tests developing a uniform probability model by assigning equal probability 1/n to each of n equally likely outcomes, calculating event probabilities as favorable/total. In a uniform model, outcomes are equally likely, like a fair die where each number has P=1/6; assign equal probability P=1/n to each, event probability is count of favorable divided by total, such as even on die {2,4,6} count 3, total 6, P=3/6=1/2, and verify probabilities sum to 1. For example, fair die {1,2,3,4,5,6}, each P=1/6, event 'even'={2,4,6}, P(even)=3/6=1/2. Here, the correct model assigns P=1/10 to each 1-10, so P(prime)={2,3,5,7} which is 4/10. A common error is including 1 as prime or missing 2, leading to wrong count or probability >1. To create the model: (1) identify equally likely outcomes (fair spinner yes), (2) count n=10, (3) assign each P=1/10, (4) verify sum=1. To calculate: (1) identify favorable primes, (2) count 4, (3) divide by 10, (4) simplify to 2/5 but 4/10 is equivalent; mistakes include wrong prime identification or not summing to 1.