If the events A and B are independent and the events A and C are independent, how about the events B and C?

Question

Are they independent or dependent events?

Is there a mathematical proof?

Answer 1

Let's say event A is "It's raining," B is "I put on shoes," and C is "I eat lunch."

Since we know that A and B are independent, we know that me putting on shoes has nothing to do with the rain. We also know that eating lunch has no cause/effect relationship with the rain. We have no way of knowing, though, whether putting on shoes is related to eating lunch. Maybe I only eat lunch with shoes on (dependent events) or maybe they have nothing to do with each other (independent.)

Answer 2

Cannot say

Example:
Event A: Occurance of the full moon
Event B: Rise in price of oil
Event C: Rise in price of gasoline

A and B are independent, A and C are independent, but C is dependent on B

Alternatively, if events A and B are as before but event C is now the collapse of some dam, then A is independent of B and C, and also B and C are also independent

Answer 3

We don't know. They may be dependent or they may not be. Look at it this way: they may actually be the same event going by two different names, we don't know. All we know is that A is independent of them.

Answer 4

P(A) P(B) = P(A ? B) via independence P(A U B) * P(A' ? B') = P(A U B) (a million - P(A U B)) P(A happens or B happens yet not the two A and B) = P(A U B) - P(A ? B) is this authentic: P(A U B) - P(A U B)^2 <= P(A U B) - P(A ? B) ? P(A U B)^2 >= P(A ? B) ? At this factor i don't think of it is authentic yet, yet then i will use independence P(A U B)^2 >= P(A) P(B) ? Now i think of it is authentic because of the fact i comprehend P(A U B) >= P(A) and P(A U B) >= P(B). consequently P(A U B)^2 >= P(A) P(B).

Answer 5

Choose a card from a deck.
A = the card is black
B = the card is a King
C= the card is a Jack

A and B as well as A and C are independent but B and C dependent

Choose one card from each of 3 decks

A = card from first deck is red
B = card from second deck s red
C card from third deck is red

Any two of these are independent

So, you can't tell