Answer: (i) 1/221 (ii) 11/221 (iii) 95/663 (iv) 1/663
Explanation:
(i) A deck of cards contains 4 Kings out of 52 total cards
1st draw: 4 Kings out of 52 total cards → 4/52 = 1/13
2nd draw: 3 remaining Kings out of 51 total remaining cards → 3/51 = 1/17
1st Draw 2nd Draw Outcome Probability
King: P(K) = 1/13 King: P(K₂/K₁) = 1/17 King, King (1/13) x (1/17) = 1/221
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(ii) A deck of cards contains 4 Jacks, 4 Queens, & 4 Kings out of 52 total cards
1st draw: 12 Face cards out of 52 total cards → 12/52 = 3/13
2nd draw: 11 remaining Face cards out of 51 total remaining cards → 11/51
1st Draw 2nd Draw Outcome Probability
Face: P(F) = 3/13 Face: P(F₂/F₁) = 11/51 Face,Face (3/13) x (11/51) = 11/221
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(iiI) A deck of cards contains 26 black cards out of 52 total cards but there are 2 black Jacks, 2 black Queens, and 2 black Kings.
1st draw: 20 Black (not Face) cards out of 52 total cards → 20/52 = 5/13
2nd draw: 19 remaining Black (not Face) cards out of 51 total remaining cards → 19/51
1st Draw 2nd Draw Outcome Probability
Black: P(B~) = 5/13 Black: P(B~₂/B~₁) = 19/51 B~,B~ (5/13) x (19/51) = 95/663
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(ii) A deck of cards contains 4 Aces out of 52 total cards
1st draw: 4 Aces out of 52 total cards → 4/52 = 1/13
2nd draw: 1 Queen of Hearts out of 51 total remaining cards → 1/51
1st Draw 2nd Draw Outcome Probability
Ace: P(A) = 1/13 Qh: P(Qh₂/A₁) = 1/51 Ace,Queen(h) (1/13) x (1/51) = 1/663