Question

Looking closely, you will see that the Jack of Spades and the Jack of Hearts are revealing only one eye. These are the “one-eyed Jacks” and are used as wild cards in a popular home-version of poker, along with the four 2’s (or “Deuces”). The King of Diamonds is also showing only one eye, so let us include it among the wild cards. That gives us a total of 7 wild cards: the four 2’s, the two one-eyed Jacks, and the single one-eyed King.

Let W denote the set of wild cards. Let J denote the set of Jacks, Q denote the set of Queens, K denote the set of kings, and H denote the set of hearts. Also, let F denote the face cards, which consist of the Jacks, Queens, and Kings.

4.1) Assume a card will be selected at random from the full deck:

(e) Is the event of drawing a Heart independent of drawing a Queen? To decide, you need to

(i) define relevant events A and B,

(ii) compute P(A) and compute P(A|B),

(iii) check to see if the two are equal or are not equal, and

(iv) state your conclusion and its grounds.

Answer #1

(e)

(i)

Let the event A be the event of drawing a Heart.

Let the event B be the event of drawing a Queen.

(ii)

P(A) = Number of Hearts the full deck / Total number of cards in the full deck

= 13 / 52

= 0.25

P(A|B) = n(A and B) / n(B) = Number of Queen Heart in the full deck / Number of Queens the full deck

= 1 / 4

= 0.25

(iii)

P(A) = P(A|B)

(iv)

As, P(A) = P(A|B) , we can consider events A and B are independent or, the event of drawing a Heart is independent of drawing a Queen.

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