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

    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 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.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.;