Let A, B, C be events such that P(A|C)=0.05 and P(B|C)=0.05. Let $\bar{A}, \bar{B}, \bar{C}$ be the complement events of A, B, C respectively. Which of the following is true?

1) $P(A\cap B|C)=(0.05)^2$
2) $P(\bar{A} \cap \bar{B}|C)\ge 0.9$
3) $P(A \cup B|C)\le 0.05$
4) $P(A \cup B|\bar{C})\ge 1-(0.05)^2 $
5) $P(A\cup B|\bar{C})\ge 0.10$

Question

Let A, B, C be events such that P(A|C)=0.05 and P(B|C)=0.05. Let $\bar{A}, \bar{B}, \bar{C}$ be the complement events of A, B, C respectively.  Which of the following is true?

1) $P(A\cap B|C)=(0.05)^2$
2) $P(\bar{A} \cap \bar{B}|C)\ge 0.9$
3) $P(A \cup B|C)\le 0.05$
4) $P(A \cup B|\bar{C})\ge 1-(0.05)^2 $
5) $P(A\cup B|\bar{C})\ge 0.10$

anonymous · Answer

@wio

anonymous · Answer

@matricked @kropot72 @SithsAndGiggles @kirbykirby

amistre64 · Answer

spose we could use some identities?
$$P(A|C)=\frac{P(A\cap C)}{P(C)}$$

amistre64 · Answer

from the looks of things:


AnC      BnC
---- = ----
   C           C

but i got no good ideas at the moment how to process it.  some things i just remain ignorant about

anonymous · Answer

Yeah I'm very confused about this question since very little information is given. But do you know maybe what a conditional probability looks like in terms of a Venn diagram? I'm not sure what "sector" would P(A|C) look like? I'm hoping maybe I'll be able to do this if I can visualize it.

amistre64 · Answer

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