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

Are they independent or dependent events?

If the events A and B are independent and the events A and C are independent, how about the events B and C?
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.)
Reply: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.
Reply: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
Reply: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