I play a card game called "Whist". In this game, all four players get 13 cards each, and you have to estimate how many tricks you will win with one trump color.
Here is my scenario: In my hand, I have 7 hearts : Ace, King, Jack, 10, ... (the rest doesn't matter). My question is : what is the probability that I will win those 7 cards if the trump is Heart? The only way for me to lose the third trick is if somebody has 3 hearts or more AND the queen. This is because if the player who has the Queen has only one or two cards he will lose it when I play my Ace and my King (people have to follow your color).
So my question is:
I know there are 6 remaining hearts in the game, they are separated into 3 players, what is the probability that one player has 3 cards or more containing the Queen?
I tried to solve it doing a probability tree but it quickly became complicated so I wonder which formula we can use.
Thanks in advance for your response!
(PS: I know that if for example I have Ace, King, Jack, 10, 8, etc, I could lose one trick if someone has 5 hearts and the 9 of hearts but I think if I am not mistaken that the probability of this is quite low (correct me if I am wrong))