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If A, B and C are mutually exclusive independent and exhaustive events then what is the probability that they occur simultaneously?
- a)1
- b)0.50
- c)0
- d)any value between 0 and 1
Correct answer is option 'C'. Can you explain this answer?
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If A, B and C are mutually exclusive independent and exhaustive events...
Mutually Exclusive, Independent and Exhaustive Events
Mutually exclusive events are events that cannot occur at the same time. For example, if a coin is flipped, it can either land heads up or tails up, but it cannot land both heads up and tails up at the same time.
Independent events are events in which the occurrence of one event does not affect the probability of the occurrence of the other event. For example, if we flip a coin twice, the outcome of the first flip does not affect the outcome of the second flip.
Exhaustive events are events that together cover all possible outcomes. For example, if we flip a coin, the possible outcomes are heads or tails, so heads and tails are exhaustive events.
Probability of Simultaneous Occurrence
If A, B, and C are mutually exclusive, independent, and exhaustive events, then the probability that they occur simultaneously is zero. This is because if they are mutually exclusive, they cannot occur at the same time. If they are independent, the occurrence of one event does not affect the probability of the occurrence of another event. And if they are exhaustive, together they cover all possible outcomes. Therefore, there are no outcomes in which all three events occur simultaneously.
So, the correct answer is option 'C' - 0.
Mutually exclusive events are events that cannot occur at the same time. For example, if a coin is flipped, it can either land heads up or tails up, but it cannot land both heads up and tails up at the same time.
Independent events are events in which the occurrence of one event does not affect the probability of the occurrence of the other event. For example, if we flip a coin twice, the outcome of the first flip does not affect the outcome of the second flip.
Exhaustive events are events that together cover all possible outcomes. For example, if we flip a coin, the possible outcomes are heads or tails, so heads and tails are exhaustive events.
Probability of Simultaneous Occurrence
If A, B, and C are mutually exclusive, independent, and exhaustive events, then the probability that they occur simultaneously is zero. This is because if they are mutually exclusive, they cannot occur at the same time. If they are independent, the occurrence of one event does not affect the probability of the occurrence of another event. And if they are exhaustive, together they cover all possible outcomes. Therefore, there are no outcomes in which all three events occur simultaneously.
So, the correct answer is option 'C' - 0.
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If A, B and C are mutually exclusive independent and exhaustive events then what is the probability that they occur simultaneously?a)1b)0.50c)0d)any value between 0 and 1Correct answer is option 'C'. Can you explain this answer?
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