I'm trying to find the probability of P5 having C1, C3, or C4. Here are the constraints of the problem.
C1 - C5: Are cards that can be held by 1 person. P1 - P5: Are players that each have 1 card. X means the person does not have the card. O means the person has the card ? means it's unknown who has the card.
P1 P2 P3 P4 P5 C1 ? X X ? ? C2 X O X X X C3 ? X X ? ? C4 ?. X. X X. ? C5 X. X. O. X. X
I've calculated by looking at each row:
C1 has a 1/3 chance of being in P5 C3 has a 1/3 chance of being in P5 C4 has a 1/2 chance of being in P5
I've calculated by looking at P5 column:
There is a 1/3 chance that they have C1, C3, or C4
I'm thinking there is a way to combine these probabilities to give me an answer as to the chance of P5 having C1, C3, or C4. Will you please show me the math and let me know what this is called in statistics?