Question

In: Statistics and Probability

I am trying to work a statistics problem for decision modeling class. The main question is:...

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 A_i 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 A_i for i= 3 to 9.

I need to know how to compute this, I need the computations step by step please Thank you.

Expert Solution

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)

orchestra answered 1 year ago

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