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, composed of

• the four 2'sk
• the two one-eyed Jacks, and
• the one-eyed King of Diamonds.

Let W denote the set of wild cards. Let C denote a club.

1) Assume a card will be selected at random from the full deck.

(a) Find P(C)

(b) Find P(C and W)

(c) Find P(C|W)

(d) Is drawing a Wild card independent of drawing a Club? State and use the definition of independence in your answer.

Baruch College, STA 9708 Prof. L. Tatum STA 9703 LN3.D Homework 3 92022 Instructions: Submit as a Word document. . E-bE-s s a. $1- 1- . in. a Q 9 go o 50 v v v $ t , E. o o o {.e o 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. I That gives us a total of 7 wild cards, composed of i the four 2'sk - the two one-eyed Jacks, and 0 the one-eyed King of Diamonds. Let W denote the set ofwild cards. Let C denote a club. 1) Assume a card will be selected at random from the full deck. (a) Find P(C) (b) Find P(C and W) (c) Find P(C|W) (d) Is drawing a Wild card independent of drawing a Club? State and use the denition of independence in your answer. 2) Try to compute P(W|C) using Bayes Rule from knowledge of P(C|W), PW ], and the other needed pieces! You welcome to try using the common-sense approach, the formal method, or both! Check your answer with the simplest method: P(W|C) = FUN and C} I P(C)