#A & B events are independent => their complements are independent

12 messages · Page 1 of 1 (latest)

plain orbit
#

I am having a little trouble trying to understand how we go from step 4 to 5 (green arrow). I understand that when we subtract A and B, we have to add the intersection of the two so we dont double count.

The intersection can be written as A intersection B or A time B.

Then that gives us the space outside the two events... Which is the complement of both A and B...

So that entire space between 1 and A&B is the complement intercept?

spark umbraBOT
plain orbit
#

this is my first time asking for help on the forum. my bad if im not doing this correctly

crisp girder
ebon vector
#

$1-P(A)-P(B)+P(A)P(B) = 1-P(A)-P(B)-P(B)(-P(A))$

fleet zephyrBOT
#

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

ebon vector
#

$=(1-P(A))(1)-P(B)[1-P(A)]$

fleet zephyrBOT
#

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

ebon vector
#

$(1-P(A))(1-P(B))$

fleet zephyrBOT
#

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

plain orbit
#

It’s the PB portion that is giving me a brain fart.

I went through it slowly with a ven diagram and in understand now. Thanks for your help guys