Question

4. There's a 20 card deck that contains 12 red cards, 4 black cards and 4 blue cards. You draw (without replacement) five cards. Let X be the number of red cards drawn and Y be the number of black cards drawn. a. Compute Cow (X,Y). b. Let W be the number of red or black cards drawn. Compute Var (W).

Answer 1

Wart! Y elonetes, the number out of 5 cards drawn in tako nalues 0,1 , 2,3,4,5 p(x=1), ('9) (8) of Red cards drawn total so x sean of . 0 6S 4 . (: 1)- :0:2383 P(x - 3) (3)(8) PO-4) 1:0.3973 125) S (2) 0.2554 PCXS) 0:0510P (0) C3) -0.0036 (X:0) 2-0.0036 E (*) - € 4p(0) = 0 (0.0036) +9L0.0543) +2(0.2393) +3 (0-3473) 36€X H4 (0-2554) +5(0.0510) = 2.9992 E (*) = & x*P(x)= 0% (0.0031) + 1° CO.Osus) +260-2383). Det +39(0.3973) *42 (0:2554) +52 COoo Sio) 59.944 i V(X) = 042 9.944-(2.9992)2 => 0.94919936

cards brown then A y denotes, the number of Black Is Sausn falee Aless, ;0,1,2,3,4 (O)(9) P(X:0) = 2 0-2817; P(X=) - - PEX =2) 2013/ .0.2167, PCX =3) (3/1 2 20.03095 P(X=4) = ((9) - 0.00103 Ely)= &YP(Y) = o(0.2817) + 1 (0.4695)+260.2167) + YEY 310.0309) +4 (0.00103) 0.99972 ECY?). Eye cy) = 021 0.2817) + 12 (0.4695) +22 (0.2167) +32(0.0309) +43 (0.00103) = 1.63088

9'63088 - (0.999722 .63088-0.99944 0.6394 con (X,Y)= (0.9491, 0.6314) ܛ ܓܥܠܺܝܠܡܬܦܐ (b ܤ ܢ ܥܕܩܫܥܝܟ ܘܪ ܣܪ ܦܠܠܩ ܝܬ ܬܩ red soul. (END A Black Forelli so p =P ( getting a Red sold ) +PC szetting a Block sold) => p = 2 => 6 => 0.8 Thess Wro (5,018) EProbality to get so sad so New)=5 (0.8) (0+2) Black isy susses] TV (W) = 0.8] [ ff x rub (hop) nou (22 zne (4-p)