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In this problem we have been given that suppose we roll a six sided dice twice.
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Now a be the event at the sum of the results is even and let b be the event that the first die result is 2.
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Now are these two events are independent? let us see how we can do it.
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So first of all let us write the sample space.
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So sample space for this very experiment will be equals to s and that s will have many values like 1 .1 and 1.
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And then here we will have 1 comma 2 and then this will continue up to 1 .6 and similarly this thing will happen with 2 .2 or we can say 2 .1.
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So here we will have 2 .2 and then we will have 2 .3 and then so on and here we have 2 .6.
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So this will go on like this in the downward side also and at last we will have 6 .1 comma 6 .2 and then here we have 6 .3 and that goes up to 6 .6.
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So this is how our sample space will look like.
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So in total the sample space will be equals to 36.
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We can say that total sample space is equals to 36.
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We will see that what is our event a, that how many elements are there in event a? so we can write event a will be equals to 1 .1 and then here we will have 1 .3 and then here we will have 1 .5 and in the similar fashion it will go on like 2 .2 and so on.
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So particularly we have to keep in mind that event a is talking about some of the results is even.
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So if we want some of the results is even, there are many numbers as such.
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3 .3 and then we will have 3 .5 and if it goes like this we will have in total many different sample many different elements in this particular event so total we will have 18 elements like 18 points will be there as such whose sum is even so we can say that number of elements in a will be equals to 18 we can write that one and check if it's 18 or not like there will be elements like 2 .6 3 .1 2 .4 4 .2 4.
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4 .6.
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5 .1.
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5.
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5 .5.
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5.
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5.
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6.
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6.
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6.
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6.
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6.
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6...