Suppose a person is chosen at random. Use your understanding about football to decide whether the event that the person weighs more than 300 pounds and the event that the person plays professional football are independent or associated.

Question

Suppose a person is chosen at random. Use your understanding about football to decide whether the event that the person weighs more than 300 pounds and the event that the person plays professional football are independent or associated.

BlackTom AI · Accepted Answer

Question restatement: We are asked to decide whether the event 'weighs more than 300 pounds' and the event 'plays professional football' are independent or associated.
Option 1: 'The two events are associated because professional football players are more likely to weigh more than 300 pounds than the average person.' This is a correct characterization: if being a football player changes the probability of weighing over 300 pounds (P(weight > 300 | football) ≠ P(weight > 300)), the events are not independent and are in fact associated. The existence of a specialized physical profile among players makes this a plausible dependence.
Option 2: 'The two events are independent because the outcome of one does not affect the outcome of the other.' This disregards how professional athletes tend to have different body types and weights due to the demands of the sport. In statistics, independence would mean P(weight > 300 | football) = P(weight > 300). Given the athletic selection and conditioning for football, this equality is unlikely, so this option is incorrect.
Option 3: 'The two events are independent because they are mutually exclusive events.' The statement that events are mutually exclusive would mean that both cannot occur at the same time. In this context, it is entirely possible (and indeed common) for a professional football player to weigh over 300 pounds, so the events are not mutually exclusive. Therefore, this justification is invalid.
Option 4: 'The two events are independent because professional football players are just as likely to weigh more than 300 pounds as the average person.' This suggests the same probability in both groups, which contradicts the idea that the player population has a distinct body type and conditioning. In reality, players may be more likely to exceed 300 pounds than the general population, making independence an incorrect claim here.
In summary, the reasoning hinges on whether the conditioning and selection in professional football alter the weight distribution relative to the general population. Since players are often heavier due to position requirements and training, the events are associated rather than independent.

Suppose a person is chosen at random. Use your understanding about football to decide whether the event that the person weighs more than 300 pounds and the event that the person plays professional football are independent or associated. Single choice

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