Probabilities of drawing certain cards

This shows the probabilities of drawing two specific cards (labeled A and B) in a hand of five cards, from decks of various sizes.

All numbers are percentages.

Deck size	A & B	A & !B	A ^ B	A | B
6	66.7	16.7	33.3	100.0
7	47.6	23.8	47.6	95.2
8	35.7	26.8	53.6	89.3
9	27.8	27.8	55.6	83.3
10	22.2	27.8	55.6	77.8
11	18.2	27.3	54.5	72.7
12	15.2	26.5	53.0	68.2
13	12.8	25.6	51.3	64.1
14	11.0	24.7	49.5	60.4
15	9.5	23.8	47.6	57.1

The probabilities of other combinations can be derived from those given in this table:

• A | !B (A or not B - possibly both conditions) is the inverse of A & !B.
• A ^ !B (A or not B but NOT both conditions) is the inverse of A ^ B.
• !A & !B (neither A nor B) is the inverse of A | B
• !A | !B (not A, or not B - possibly both conditions) is the inverse of A & B.
• !A ^ !B (not A, or not B, but NOT both conditions) is logically the same as A ^ B.