Question

Draw three cards without replacement from a deck of cards. Let H be the number of hearts and S the number of spades drawn.

(a) Find the joint pmf of (H, S)

(b) Find P(H = S)

Answer 1

a) Note hat, a deck contains 52 carrds. The number o ways 3 car d s can be da wihou weplacement from 52 cand s mS2 ar ds ttere H d enokes he number of hearrs and S denohes he number of Spades e value s O, l/ 2, 3 and ScanrakeHe values 2, 3 sweh tha

The numben of othen cards - 52-(13 +13) 26 Now, he nunben of way s3 cards ean be drawn sueh hat there avex number of earts, y num beve 0 an d spa de s of.MAanst taktig (3-χ-y) n'n m b en other cards 13 1 3 2 6 The joint pmf of (H, S) s 1 3 2 6 (χ 3-х-у 5 2 y:0(リ3 3

1 3 2 6 3-0-0 5 2 2 1 3 1 3 9) 5 2 2 6 0 0 4 394 22100 22 100 6994 - 03)65. 2 2 100