Suppose a person is randomly selected. Are the following two events mutually exclusive or not mutually exclusive?

Event A: The person is taller than 63 inches.

Even B: The person is healthy.

Choose the correct answer below.

Question

Suppose a person is randomly selected. Are the following two events mutually exclusive or not mutually exclusive?

Event A: The person is taller than 63 ​inches.

Even B: The person is healthy.

Choose the correct answer below.

BlackTom AI · Accepted Answer

To tackle this question, I’ll examine what it means for two events to be mutually exclusive: they cannot both occur at the same time. If there is any possibility of both happening together, the events are not mutually exclusive.

Option 1: 'The pair of events is not mutually exclusive because being taller than 63 inches has no effect on whether or not the person is healthy.' This statement asserts not mutual exclusivity, but it grounds the claim in the idea that height has no effect on health. The underlying assertion is that there is some overlap, but the justification is weak: whether height affects health is not the point; what matters is whether both conditions can occur simultaneously. Even if height has no causal effect on health, a tall person can still be healthy, so the pair can occur together. However, labeling the reason as 'has no effect' is making a causal claim that isn’t strictly necessary to determine mutual exclusivity, and the sentence also treats 'not mutually exclusive' as if it requires a demonstration of overlap, which is the correct broad idea but the justification is muddled.

Option 2: 'The pair of events is not mutually exclusive because someone can be taller than 63 inches and healthy.' This directly states that both conditions can occur at once, which is exactly what non–mutually exclusive means. It provides a clear overlap scenario: a person can satisfy both A (taller than 63 inches) and B (healthy) simultaneously. This is a correct characterization of the relationship between A and B.

Option 3: 'The pair of events is mutually exclusive because being taller than 63 inches has no effect on whether or not the person is healthy.' This asserts mutual exclusivity, which would require that the two events cannot occur together. Yet there exist healthy tall individuals, so this claim is false in general. The reasoning also again uses the idea that height has no effect, which doesn’t logically force exclusivity.

Option 4: 'The pair of events is mutually exclusive because someone cannot be taller than 63 inches and healthy.' This is the strongest incorrect stance: it states the opposite of what is true by claiming an impossibility. There exist people who are both taller than 63 inches and healthy, so this is simply incorrect.

In summary, the correct understanding is that the events are not mutually exclusive because there is possible overlap (a person can be taller than 63 inches and healthy). The second option explicitly captures that overlap, while the other options mischaracterize the relationship or rely on unsupported causal claims about height and health.

251A-STATS-10-LEC-1 Quiz #5- Requires Respondus LockDown Browser

Suppose a person is randomly selected. Are the following two events mutually exclusive or not mutually exclusive? Event A: The person is taller than 63 inches. Even B: The person is healthy. Choose the correct answer below.

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