If $P(A) = 0.4$, $P(B) = 0.7$, and $P(A \cap B) = 0.2$, what is the value of $P(A \cup B)$
(I'm lost pls help)

Question

If $P(A) = 0.4$, $P(B) = 0.7$, and $P(A \cap B) = 0.2$, what is the value of $P(A \cup B)$
(I'm lost pls help)

notmeta · Answer

I know the answer of the question but I need to know how to solve it.

Breathless · Answer

hold on

Breathless · Answer

addition rule of probability as so you would take A and B and do A+B as of which it doesn't matter what numbers u put in those spots all we care about is subtracting the other number, so if 0.7+0.4 is what we have then we will minus it by 0.2 so in turn we have 0.7+0.4-0.2 which equals 0.9

Breathless · Answer

if not am stumped

Breathless · Answer

here's what Google has to say:

To find the value of $P(A \cup B)$, you use the Addition Rule for probability.

The Formula:$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

The Calculation:Plug in your values: $0.4 + 0.7 - 0.2$
Add the individual probabilities: $0.4 + 0.7 = 1.1$
Subtract the intersection: $1.1 - 0.2 = 0.9$The value of $P(A \cup B)$ is 0.9.

Why do we subtract $P(A \cap B)$?

Think of it like two overlapping circles in a Venn diagram:When you add $P(A)$ and $P(B)$ together, you are counting the area where they overlap (the intersection) twice.To get the correct total area (the union), you have to subtract that overlap once so it's only counted once.

adrianluvvsyouu2 · Answer

P(a) + P(b) - P(a and b) = p(a or b)

p(a and b) represents the overlap where both events are true, which means we don't want to add that to our total probability if we just want the chance of one event happening at a time.

adrianluvvsyouu2 · Answer

@breathless wrote:

here's what Google has to say: To find the value of $P(A \cup B)$, you use the Addition Rule for probability. The Formula:$P(A\cup B)=P(A)+P(B)-P(A\cap B)$ The Calculation:Plug in your values: $0.4 + 0.7 - 0.2$ Add the individual probabilities: $0.4 + 0.7 = 1.1$ Subtract the intersection: $1.1 - 0.2 = 0.9$The value of $P(A \cup B)$ is 0.9. Why do we subtract $P(A \cap B)$? Think of it like two overlapping circles in a Venn diagram:When you add $P(A)$ and $P(B)$ together, you are counting the area where they overlap (the intersection) twice.To get the correct total area (the union), you have to subtract that overlap once so it's only counted once.

If he wanted google AI why wouldn't he just use google AI, I don't understand the point of answering questions like this

adrianluvvsyouu2 · Answer

@adrianluvvsyouu2 wrote:

P(a) + P(b) - P(a and b) = p(a or b) p(a and b) represents the overlap where both events are true, which means we don't want to add that to our total probability if we just want the chance of one event happening at a time.

|dw:1778531715963:dw| That center piece is the probability of both A and B being true, but when we say "A or B" we don't want to include that. I hope the visual helps you understand this