Let us understand mutually exclusive events with another example. Let us consider one throw of a fair dice. These are the six possible outcomes. At one throw, you have to get one of these. Let us consider two events, ‘A’ and ‘B’ and understand if they are mutually exclusive or not. Event ‘A’ is getting an even number. And event ‘B’ is getting an odd number. Remember, we have to consider just one throw. Assume we get a two at the first throw. It is even and not odd at the second throw we get a 5. So it is odd and not even. This means that if we get an odd number, we know that it is not even. And if we get an even number it cannot be odd. These two events cannot occur together and are hence mutually exclusive events. Now let’s look at another case. Say event ‘A’ is getting an odd number. And event ‘B’ is getting a number less than four. Are these events mutually exclusive? Let’s see! If we get a 1 then we can see that it’s an odd number as well as a number less than 4. It’s the same if we get a 3. These two events can happen together which tells us that they are not mutually exclusive. Many get confused between Independent and mutually exclusive events. If you are one among those, just remember these two simple things. Two events are independent if they are not related. That is the outcome of one does not affect the other. They are totally unrelated. And two events are mutually exclusive if they cannot occur together. If one event occurs, the other just cannot occur. So yes, an event cannot be independent and mutually exclusive at the same time. Because if they’re independent they may occur together. And if they are mutually exclusive one event will be dependent on the other. That is, if one occurs, the other one will not occur.

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A fair die is tossed eight times. Probability that on the eight throw a third six is observed is…

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1:05 No since they are not mutually exclusive since 3 is less than 4, YET, it is odd, so both can occur simultaneously. Tall and Short , Night and Day are mutually exclusive, but tall and rich or or cold and night (night being cold/winter) are not mutually exclusive or a person being investigated for more than one things ( those things are not mutually exclusive ie being pursued as a spy doesn't mean it prevents you from being pursued as robbing a bank or being pursued for soliciting prostitutes). All three can occur at the same time.

However, they only could be mutually exclusive if there is some country on the planet where the law is , 'a person can only be pursued for one offense , so if he/she solicits prostitute FIRST, then he cannot be prosecuted for anything after that such as for bank robbery,, spying and others. Of course there is no such thing and will never be such a thing.

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