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:

(f) Find P(W), P(F), and P(W|F). (Note there are 7 wild cards.) Is the event of drawing a Wild card independent of drawing a Face card?

Explain in words what independence would mean.

Answer 1

Probability=The number of wanted outcomes/The number of possible outcomes

given:

no of wild cards= 7

W denote the set of wild cards.

F denote the face cards, which consist of the Jacks, Queens, and Kings.( tehre are total 4*3= 12 face cards). thus,

now set (W&F) and contains the two one-eyed Jacks, and the single one-eyed King = 3 cards hence,

Two events are independent, statistically independent, if the occurrence of one does not affect the probability of occurrence of the other.

mathematically =

thus in our case we have to find if

as calculated above we have

and  ,

THUS CLEARLY

this means that the event of drawing a Wild card is not independent of drawing a Face card. Thus if we draw the face (wild card) first in the first draw and keep it aside and draw the next card we will alter the probability of drawing the wild card/(face card), since both are not independent events.