One deck of cards is numbered 1 - 13 and a second deck of cards is numbered 1-10

Question

One deck of cards is numbered 1 - 13 and a second deck of cards is numbered 1-10. A card is drawn from the 13 card deck, then from the 10 card deck. Find the probability: 1) a- Plan even # and an odd #) b. P(not 8 and a multiple of 2) c. Pla multiple of 3 and a even #) A jar contains 15 marbles. 5 black, 4 yellow, 3 blue, and 3 purple. Two marbles are drawn with replacement. What is the probability: 2) a. P(black and blue) b. P(yellow or purple, and then blue) c. P(not purple and black) or not blue) 3) You have a standard deck of cards. Two cards are drawn without replacement. What is the probability: a. P(king and ace) b.p6orygivenred cards c. P(2 and 3 given diamonds) d. P(S or 6 or 7 and a jack) e, p (even # or a red card) 4) A: (1,3,5,7,8) a) Find A n C b) Find CnB c) Find An d) Find Cu e) Find An Be f) Find P(BUA) B: 12,3,7,9 U: (1,2,3,4,5,6,7,8,9,10) 5) The table shows the number (in thousands) of earned degrees conferred in the United States in the year 2004 level and gender Male Female Total Associate 255 305 Bachelor's

Explanation / Answer

#1.
a)
An even number card can be drawn from 1st deck in 6C1 ways. and its probability is 6/13

An odd numbered card can be drawn from 1st deck in 7C1 ways and its probability is 7/13

An even number card can be drawn from 2nd deck in 5C1 ways. and its probability is 5/10

An odd numbered card can be drawn from 2nd deck in 5C1 ways
and its probability is 5/10

P(an even # and an odd #) = 6/13*5/10 + 7/13*5/10 = 0.5

b)
P(Not 8 from 1st Deck) = 12/13
P(multiple of 2 from 1st deck) = 6/13
P(Not 8 from 2nd Deck) = 9/10
P(multiple of 2 from 2nd deck) = 5/10

P(not 8 and a multiple of 2) = 12/13*5/10 + 6/13*9/10 = 0.8769

c)
P(a multiple of 3 from 1st Deck) = 4/13
P(A even from 1st deck) = 6/13
P(a multiple of 3 from 2nd Deck) = 3/10
P(a even from 2nd deck) = 5/10

P(a multiple of 3 and a even) = 4/13*5/10 + 6/13*3/10 = 0.2923

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