Can two events with nonzero probabilities be both independent and mutually exclusive? Explain your reasoning.

Can two events with nonzero probabilities be both independent and mutually exclusive? Explain your reasoning.

Answers (1)

Two events are mutually exclusive if they cannot occur at the same time. Two events are independent if the occurrence of one of the events does not influence the occurrence of the other event. Thus two events cannot be both at the same time, because if one of the events occur, then we now that the other event does not occur and thus the second event is influenced by the first event occurring.
Result: No

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This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
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If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
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Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
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