Larger probability numbers indicate greater likelihood. Since 0.91 > 0.49 > 0.03, the correct order from most likely to least likely is 0.91, 0.49, 0.03. Choice A shows least to most likely. Choices C and D have incorrect orderings.

An event that is neither likely nor unlikely has probability around 1/2 = 6/12. Small prize: 5/12 < 6/12, Large prize: 1/6 = 2/12 < 6/12. Both are less than 1/2. Choice B incorrectly states small prize is more likely. Choices C and D incorrectly compare the probabilities to 1/2.

When you encounter probability questions, you need to interpret what the numerical value actually means in real-world terms. Converting fractions to decimals often makes this interpretation clearer.

First, let's convert $$\frac{11}{50}$$ to a decimal: $$\frac{11}{50} = 0.22 = 22%$$. This means that out of every 100 products, about 22 would have defects while 78 would not. Since significantly more products (78%) are defect-free than defective (22%), products are unlikely to have defects. Answer D correctly identifies this pattern and explains that 0.22 is relatively close to zero.

Let's examine why the other choices miss the mark. Choice A makes a logical error—just because a probability is greater than zero doesn't mean an event is likely. Most probabilities are greater than zero, but many events remain unlikely. Choice B incorrectly calls $$\frac{11}{50}$$ a "large fraction" when it's actually less than half, making it relatively small. Choice C suggests equal chances (50-50), but $$\frac{11}{50} = 22%$$ is nowhere near 50%.

The key insight is understanding probability ranges: values close to 0 indicate unlikely events, values around 0.5 suggest roughly equal chances, and values close to 1 indicate likely events. Since 0.22 is much closer to 0 than to 0.5, the event is unlikely.

Study tip: Always convert fractions to percentages in probability problems—it makes interpretation much clearer. Remember that "unlikely" doesn't mean "impossible," just that the event happens less than half the time.

When you encounter probability questions, remember that probabilities range from 0 to 1, where values closer to 1 indicate more likely events and values closer to 0 indicate less likely events. The key threshold is 0.5 (or 50%) - this is the dividing line between likely and unlikely events.

A probability of 0.6 means the event has a 60% chance of occurring. Since 0.6 is greater than 0.5, this event is actually likely to happen, not unlikely. The student's reasoning contains a fundamental misunderstanding: they correctly identified that 0.6 is "more than half" but then incorrectly concluded this means the event "probably won't happen." In reality, when something is more than half likely, it probably will happen.

Looking at the wrong answers: Choice A incorrectly states that 0.6 is impossible - probabilities between 0 and 1 are perfectly valid. Choice B suggests the format matters for determining likelihood, but whether you write 0.6 or 60%, the likelihood remains the same. Choice C contains the same error as the student's original reasoning, claiming unlikely events have probabilities above 0.5, which is backwards.

Choice D correctly identifies that probabilities above 0.5 indicate likely events, making this event probable rather than improbable.

Study tip: Remember the 0.5 rule - probabilities above 0.5 mean "likely" (more than 50-50 odds), while probabilities below 0.5 mean "unlikely." Don't let the decimal format confuse you; 0.6 = 60% = likely.

A probability near 0 indicates an unlikely event. 0.15 is close to 0, making it unlikely but not impossible. Choice B (0.48) is close to 1/2, indicating neither unlikely nor likely. Choice C (0.52) is also close to 1/2 and slightly likely. Choice D (0.85) is close to 1, indicating a likely event.

7/8 = 0.875, which is very close to 1. Probabilities near 1 indicate likely events. Choice A incorrectly focuses on the denominator size. Choice B incorrectly suggests the format affects likelihood. Choice D incorrectly states probabilities must be whole numbers.

The reasoning is correct. 1/3 ≈ 0.33 is closer to 0 than to 1, and since it's well below 0.5, it indicates an unlikely event. Choice A oversimplifies the definition. Choice B incorrectly states 0.33 is close enough to 0.5 to be likely. Choice D incorrectly suggests fractions can't be classified.

Converting to decimals: 40% = 0.40, 3/8 = 0.375, and 0.42 = 0.42. Since 0.42 > 0.40 > 0.375, Player C is best. Choice A incorrectly assumes fractions are always largest. Choice C incorrectly treats different values as equal. Choice D compares the numerical digits rather than the actual values.

This question tests understanding probability as a number between 0 and 1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling a 1 on a die has P=1/6≈0.17 (1 favorable out of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing a non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 out of 52 non-Ace, 92% chance); rolling a 7 is impossible P=0 (no 7 on standard die). The correct probability is 1/6≈0.17 (unlikely) as there is 1 favorable outcome out of 6 equally likely ones. A mistake is claiming P=1.5 (likely), but probabilities can't exceed 1; or confusing with impossible (P=0) when it is possible but unlikely. Steps: (1) sample space {1,2,3,4,5,6}, (2) favorable: {1}, (3) P=1/6, (4) unlikely since <0.5, (5) near 0 on line. Unlikely means possible but low chance, unlike impossible.

This question tests understanding probability as a number between 0 and 1 indicating event likelihood: 0 means impossible, near 0 means unlikely, 1/2 means equally likely as not, near 1 means likely, and 1 means certain, with larger numbers meaning greater likelihood. On the probability scale from 0 to 1, impossible events have P=0 (cannot occur, like rolling a 7 on a standard die), certain events have P=1 (must occur, like rolling a number from 1 to 6 on a die which covers all outcomes), unlikely events have P near 0 (like P=0.1 or 1/10, could happen but probably won't), equally likely events have P=1/2 (50-50, like a coin flip landing heads), and likely events have P near 1 (like P=0.9, probably will occur); larger probabilities indicate greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%), and on a number line, probabilities are plotted from 0 (left, impossible) to 1 (right, certain) with 1/2 at the center (neither unlikely nor likely). For example, rolling a 1 on a die has P=1/6≈0.17 (1 favorable out of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads has P=1/2 (equally likely as tails, 50-50); drawing a non-Ace from a deck has P=48/52≈0.92 (likely—only 4 Aces so 48 out of 52 are non-Ace, 92% chance); rolling a 7 is impossible with P=0 (no 7 on a standard die). In this case, 0.75 should be located three-quarters of the way from 0 to 1, closer to 1, indicating likely. A common error is placing it near 0 because 0.75<1/2 (wrong, since 0.75>0.5) or at 1/2 because 0.75=0.5 (incorrect equality), or to the right of 1 because >1 (but probabilities can't exceed 1). To use probability: (1) identify the event and sample space, (2) count favorable and total outcomes, (3) calculate P=favorable/total, (4) interpret (e.g., 0.75 near 1, likely), (5) locate on the 0-1 scale (three-quarters toward 1). Comparing probabilities: larger means more likely (if P(rain)=0.3 and P(sun)=0.7, sun is more likely since 0.7>0.3); complementary events sum to 1 (if P(A)=0.3, P(not A)=0.7); impossible (P=0 exactly, like rolling 7) differs from unlikely (P>0 but near 0, like rolling 1); mistakes include probabilities outside 0-1, wrong likelihood categories, backward comparisons, or confusing percent with probability.