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# View of /trunk/NationalProblemLibrary/Rochester/setProbability3Events/ur_dis_9_18.pg

Thu May 4 16:40:05 2006 UTC (7 years ago) by jjholt
File size: 1476 byte(s)
Added tags.  --JH


    1 ## DESCRIPTION
2 ##   Compute Discrete Probabilities
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Probability', 'Discrete')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Algebra')
9 ## DBchapter('Counting and Probability')
10 ## DBsection('Probability')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
31
32 BEGIN_TEXT
33 A five-card poker hand is dealt at random from a standard 52-card deck.
34 $BR Note the total number of possible hands is C(52,5)=2,598,960.$BR
35 Find the probabilities of the following scenarios: $BR 36 (a) What is the probability that the hand contains exactly one ace?$BR
37 Answer=$$\frac{\alpha}{C(52,5)},$$ where $$\alpha=$$ \{ ans_rule(30)
38 \}
39 $PAR 40 (b) What is the probability that the hand is a flush? (That is all the 41 cards are 42 of the same suit: hearts, clubs, spades or diamonds.)$BR
43 Answer=$$\frac{\beta}{C(52,5)},$$ where $$\beta=$$
44 \{ ans_rule(30) \}
45 $PAR 46 (c) What is the probability that the hand is a straight flush?$BR
47 Answer=$$\frac{\gamma}{C(52,5)},$$ where $$\gamma=$$
48 \{ ans_rule(30) \}
49 \$PAR
50 END_TEXT
51
52 ANS(num_cmp( 778320 ) );
53 ANS(num_cmp( 5148 ) );
54 ANS(num_cmp( 40 ) );
55
56 ENDDOCUMENT();        # This should be the last executable line in the problem.;