3 years ago

What must be true in order for p (a or b) = p(a) + (b)

1 answer:

7 0

A and B must be disjoint. You have, by the inclusion/exclusion principle, that

$\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cap B)$

where the last term is required to prevent double counting. When $A$ and $B$ are disjoint, you have $A\cap B=\emptyset$ and $\mathb P(A\cap B)=0$ , leaving you with

$\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)$

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How would you describe domain

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Answer:

The domain represents the x-axis, more specifically, what is happening on the x-axis. So when looking at a graph, if you are asked to find the domain think about what the x-axis looks like. I put an image in to show you an example of what the domain would be for a parabola:

So on the left side of the x-axis, we can see that the line stretches out into negative infinity, so the domain would begin at negative infinity.

On the right side of the x-axis, the parabola also stretches into positive infinity, so here the domain would be (negative infinity, positive infinity), because it goes to both ends forever.