# True or False? If events A and B independent then A and B disjoint. Explain your answer. If false, give a counter example. If true, prove the statement.

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True or False? If events A and B independent then A and B disjoint. Explain your answer. If false, give a counter example. If true, prove the statement.

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Step 1

Independent events:

Two or more events are said to be independent if occurrence of one does not affect the occurrence of other. In other words, it can be said that, independent events do not affect the probability of occurrence of one another. That is, independent events can happen at the same time.

Let A and B are two events, then the probability of occurrence of the event A will not affect the probability of occurrence of the event B.

Example:

• Getting a head in the first toss of a coin and getting a tail in the second toss of a coin.

The union, intersection and conditional probabilities of independent events are given below:

Step 2

Disjoint events:

Disjoint events are also known as mutually exclusive events. Any two events are said to be mutually exclusive if it is not possible to occur them together. That is, the events will not happen at the same time.

Let A and B are two events, then the two events A and B will not have any element or outcome in common.

Example:

• Getting head and tail in the same toss of a coin.

The union, intersection and conditional probabilities of disjoint events are given below:

Step 3

Check whether the given statement is true or false:

From the definitions of independent events and disjoint events, it is clear that any two independent events can never be disjoint except if one of the two events is impossible or null.

Since, the probability of an impossible event is “0”. If one of the two events is null or impossible then the ...

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