document.write( "Question 1058405: Q.1 Two cards are drawn from a well shuffled deck of 52 cards
\n" ); document.write( "without replacement. Determine the probability of each event:
\n" ); document.write( "a) Both cards are spades.
\n" ); document.write( "b) The second card is a spade.
\n" ); document.write( "c) At least one card is a red card.
\n" ); document.write( "d) The first card is a face and the second card is a diamond.\r
\n" ); document.write( "\n" ); document.write( "Q.2 One fair black die and one fair white die are rolled. Use
\n" ); document.write( "the sample space, shown below, to answer the following Questions:
\n" ); document.write( "What is the Probability:-
\n" ); document.write( "a) The sum of the two dice is 9?
\n" ); document.write( "b) That the sum of the two dice is a least 4?
\n" ); document.write( "c) That the Quotient of the two dice is 3?
\n" ); document.write( "d) That the white die is three less than the black die?
\n" ); document.write( "e) Of getting an odd number on both dice?
\n" ); document.write( "g) Of obtaining the same number on each die if it is known that
\n" ); document.write( "the sum of the two dice is at most 7?\r
\n" ); document.write( "\n" ); document.write( "Q.3 Five cards are dealt from a well-shuffled deck of 52 cards.
\n" ); document.write( "What is the Probability that the hand will contain:
\n" ); document.write( "a) 2 tens and 3 fives?
\n" ); document.write( "b) Exactly 3 twos and two other cards that are not twos?
\n" ); document.write( "c) Three of a kind?(three cards the same and the other cards not
\n" ); document.write( "the same as the three of a kind and not the same as each other?\r
\n" ); document.write( "\n" ); document.write( "Thanks!
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #673484 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
Q.1 Two cards are drawn from a well shuffled deck of 52 cards
\n" ); document.write( "without replacement. Determine the probability of each event:
\n" ); document.write( "a) Both cards are spades.
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\r\n" );
document.write( "P(first is a spade)*P(second is a spade)\r\n" );
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document.write( "(13/52)(12/51) = 1/17\r\n" );
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\n" ); document.write( "b) The second card is a spade.
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\r\n" );
document.write( "1/4   The probability of any randomly draw card is a spade is always 1/4.\r\n" );
document.write( "      The probability would change once we knew what the first card was, but\r\n" );
document.write( "      we have no way of knowing that.\r\n" );
document.write( "

\n" ); document.write( "c) At least one card is a red card.
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\r\n" );
document.write( "1 - the probability that they are both from the 39 non-spades.\r\n" );
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document.write( "1 - (39/52)(38/51) = 15/34 \r\n" );
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\n" ); document.write( "d) The first card is a face and the second card is a diamond.
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\r\n" );
document.write( "Case 1:  The first is a diamond face card.\r\n" );
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document.write( "(3/52)(12/51) = 1/68\r\n" );
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document.write( "Case 2:  The first is a non-diamond face card.\r\n" );
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document.write( "(9/52)(13/51) = 3/68\r\n" );
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document.write( "Answer = Their sum = 1/68 + 3/68 = 1/17 \r\n" );
document.write( "

\n" ); document.write( "Q.2 One fair black die and one fair white die are rolled.
\n" ); document.write( "Use the sample space, shown below, to answer the following Questions:
\n" ); document.write( "
\r\n" );
document.write( "We'll assume the number on the left of each ordered pair is the\r\n" );
document.write( "black die and the one on the right of each ordered pair is the\r\n" );
document.write( "white die.  That won't make any difference in some of these \r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)  \r\n" );
document.write( "

\n" ); document.write( "What is the Probability:-
\n" ); document.write( "a) The sum of the two dice is 9?
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
document.write( "\r\n" );
document.write( "Those 4 ways colored red out of 36, or 4/36 = 1/9  \r\n" );
document.write( "

\n" ); document.write( "b) That the sum of the two dice is a least 4?
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\r\n" );
document.write( "All but the 3 rolls (1,1), (1,2), and (2,1).\r\n" );
document.write( "That's 33 out of 36 or 33/36 or 11/12\r\n" );
document.write( "

\n" ); document.write( "c) That the Quotient of the two dice is 3?
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\r\n" );
document.write( "Only (3,1) or (6,2).  That's 2 ways out of 36 or 2/36 or 1/18\r\n" );
document.write( "

\n" ); document.write( "d) That the white die is three less than the black die?
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\r\n" );
document.write( "That's (6,3), (5,2), (4,1).  That's 3 out of 36 or 3/36 or 1/12.\r\n" );
document.write( "

\n" ); document.write( "e) Of getting an odd number on both dice?
\n" ); document.write( "
\r\n" );
document.write( "Half the numbers on a die are odd.  The probability that\r\n" );
document.write( "the black die will be odd is 1/2, and the probability that\r\n" );
document.write( "the white die is odd is also 1/2.\r\n" );
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document.write( "So probability = (1/2)(1/2) = 1/4\r\n" );
document.write( "

\n" ); document.write( "g) Of obtaining the same number on each die if it is known that
\n" ); document.write( "the sum of the two dice is at most 7?
\n" ); document.write( "
\r\n" );
document.write( "Since we know that the sum is at most 7, we reduce the sample \r\n" );
document.write( "space to:\r\n" );
document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5)  \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4)  \r\n" );
document.write( "(4,1) (4,2) (4,3)  \r\n" );
document.write( "(5,1) (5,2)  \r\n" );
document.write( "(6,1)  \r\n" );
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document.write( "Those 3 red ones out of 21.  That's 3/21 = 1/7 \r\n" );
document.write( "

\n" ); document.write( "Q.3 Five cards are dealt from a well-shuffled deck of 52 cards.
\n" ); document.write( "What is the Probability that the hand will contain:\r
\n" ); document.write( "\n" ); document.write( "a) 2 tens and 3 fives?
\n" ); document.write( "
\r\n" );
document.write( "(4C2)(4C3) = (6)(4) = 24 ways out of 52C5 \r\n" );
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document.write( "That's 24/2598960 = 1/108290\r\n" );
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\n" ); document.write( "b) Exactly 3 twos and two other cards that are not twos?
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\r\n" );
document.write( "(4C3)(48C2) = (4)(1128) = 4512 out of 52C5\r\n" );
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document.write( "That's 4512/2598960 = 94/54145\r\n" );
document.write( "

\n" ); document.write( "c) Three of a kind?(three cards the same and the other cards
\n" ); document.write( "not the same as the three of a kind and not the same as each other?
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\r\n" );
document.write( "Choose the Rank of the three 13C1 = 13 ways\r\n" );
document.write( "Choose the Suits of the three 4C3 = 4 ways\r\n" );
document.write( "Choose the ranks of the other two 12C2 = 66 ways\r\n" );
document.write( "Choose the suit of the lower ranking one of those two = 4C1 = 4 ways\r\n" );
document.write( "Choose the suit of the higher ranking one of those two = 4C1 = 4 ways\r\n" );
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document.write( "That's (13)(4)(66)(4)(4)=54912 ways out of 52C5\r\n" );
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document.write( "That's 54912/2598960 = 88/4165\r\n" );
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document.write( "Edwin

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