In: Statistics and Probability
I am trying to work a statistics problem for decision modeling class. The main question is:
Consider the experiment of drawing two cards without replacement from a deck consisting of only the ace through 10 of a single suit (for example, only hearts).
Q - Define the event Ai to be the set of outcomes for which the sum of the values of the cards is i (with an ace = 1). List the outcomes associated with Ai for i= 3 to 9.
I need to know how to compute this, I need the computations step by step please Thank you.
The deck consists of only the ace through 10 of a single suit. So, the numbers on each card are 1 (for Ace), 2, 3, 4, 5, 6, 7, 8, 9, 10
The sum of the values of the two cards drawn without replacement will be in between 3 to 19. The minimum possible number is 3 (1 + 2) . The maximum possible number is 19 (10 + 9) .
The outcomes associated with A3 are (1, 2) (2, 1)
The outcomes associated with A4 are (1, 3) (3, 1)
The outcomes associated with A5 are (1, 4) (2, 3) (3, 2) (4, 1)
The outcomes associated with A6 are (1, 5) (2, 4) (4, 2) (5, 1)
The outcomes associated with A7 are (1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)
The outcomes associated with A8 are (1, 7) (2, 6) (3, 5) (5, 3) (6, 2) (7, 1)
The outcomes associated with A9 are (1, 8) (2, 7) (3, 6) (4, 5) (5, 4) (6, 3) (7, 2) (8, 1)
The outcomes associated with A10 are (1, 9) (2, 8) (3, 7) (4, 6) (6, 4) (7, 3) (8, 2) (9, 1)
The outcomes associated with A11 are (1, 10) (2, 9) (3, 8) (4, 7) (6, 5) (7, 4) (8, 3) (9, 2) (10, 1)
The outcomes associated with A12 are (2, 10) (3, 9) (4, 8) (5, 7) (7, 5) (8, 4) (9, 3) (10, 2)
The outcomes associated with A13 are (3, 10) (4, 9) (5, 8) (6, 7) (7, 6) (8, 5) (9, 4) (10, 3)
The outcomes associated with A14 are (4, 10) (5, 9) (6, 8) (8, 6) (9, 5) (10, 4)
The outcomes associated with A15 are (5, 10) (6, 9) (7, 8) (8, 7) (9, 6) (10, 5)
The outcomes associated with A16 are (6, 10) (7, 9) (9, 7) (10, 6)
The outcomes associated with A17 are (7, 10) (8, 9) (9, 8) (10, 7)
The outcomes associated with A18 are (8, 10) (10, 8)
The outcomes associated with A19 are (9, 10) (10, 9)