Question

if P(A) is independent of P(BnC) is P(A) independent of P(B) and of P(C) when P(B) and P(C) are not necessarily independent?

Answer 1

is this the exact question as written? it makes no sense,
\[P(A)\] is a number, as is \(P(A\cap B)\)
numbers are not sets, they are numbers and as such it makes so sense to ask if two numbers are "independent"

Answer 2

Thats not the question asked but, I guess i mean A is independent of the intersection of B n C. Does that make A independent of B and A independent of C?

Answer 3

Here is the problem I'm trying to solve

Answer 4

\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]

Answer 5

you have all the numbers on the right, plug them in

Answer 6

I don't have P(A) or P(B) though

Answer 7

ooh i see
lets see if we can find them, give me a minute
i bet a venn diagram might work well

Answer 8

Yea this questions really hard I think

Answer 9

I tried doing something like that but I couldn't get enough things to cancel out.

Answer 10

one second
it is totally doable
we need to start in the center with
\[P(O\cap E\cap F)\]

Answer 11

since you are told \(O\) and \(E\cap F\) are independent, that means
\[P(O\cap E\cap F)=P(O)\times P(E\cap F)=0.5\times .125=.0625\]

Answer 12

yes i got that

Answer 13

now i am stuck again damn

Answer 14

oh maybe i have an idea now

Answer 15

nicee

Answer 16

this is taking a lot of paper, maybe i am missing something obvious

Answer 17

thats why i was asking my original question, because I thought I was missing something like that

Answer 18

damn i keep getting one more variable than i can get equations!!

Answer 19

ok i am stuck

Answer 20

I made the assumption i was asking about and got an answer i think is too low.

Answer 21

nvm i made a mistake

Answer 22

ok i fixed it and i got .675 as my answer which seems pretty legit

Answer 23

question 26 is identical except for the numbers
there does seem to be another assumption made that we did not use

Answer 24

Thats what i used

Answer 25

perhaps it was in the wording
i took "the need for orthodontal work is indpendent for the need of filling and extraction" to mean
\[P(O|E\cap F)=P(O)\] but they seem to have interpreted it differently as independent one at a time

Answer 26

yikes

Answer 27

yes i interpreted it that way as well. what im wonderig is if they are both true. ill let you know if i figure it out. g2g though thanks for your help :)