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If we flip a coin twice is the event of having an odd

Question: If we flip a coin twice, is the event of having an odd number of heads independent of the event that the first flip comes up heads? Is it independent of the event that the second flip comes up heads? Would you say that the three events are mutually independent? (This hasn't been defined, so the question is one of opinion. However you should back up your opinion with a reason that makes sense!)

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Mathematics: If we flip a coin twice is the event of having an odd

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