function [] = chap_3_prob_28()
%
% Written by:
% --
% John L. Weatherwax 2006-08-28
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
%-----
format rat
% Part (a):
%
% for p(F):
%
% the first 19 cards are not aces:
firstPart = prod( 48 : -1 : ( 48-19+1 ) );
% the 20th card is an ace:
midPart = 4;
% the remaining cards can be anything:
lastPart = factorial( 52-20 );
num = firstPart * midPart * lastPart ;
den = factorial( 52 );
pF = num/den;
disp(pF)
% for P(EF):
%
% the first 19 cards are not aces:
firstPart = prod( 48 : -1 : ( 48-19+1 ) );
% the 20th card is an ace (but not the ace of spades):
midPart = 3;
% the 21st card is the ace of spades:
midPart2 = 1;
% the remaining cards can be anything:
lastPart = factorial( 52-21 );
num = firstPart * midPart * midPart2 * lastPart ;
den = factorial( 52 );
pEF = num/den;
disp(pEF)
% the probability we want:
%
pEF/pF
% Part (b):
%
% P(EF) is now some what different:
%
% the first 19 cards are not one of the four aces or the two of clubs
firstPart = prod( 47 : -1 : ( 47-19+1 ) );
% the 20th card is any ace:
midPart = 4;
% the 21st card is the two of clubs:
midPart2 = 1;
% the remaining cards can be anything:
lastPart = factorial( 52-21 );
num = firstPart * midPart * midPart2 * lastPart ;
den = factorial( 52 );
pEF = num/den;
disp(pEF)
% using this the probability we want is given by
%
pEF/pF
% the second method:
%
pA1CA2C = prod( 30:48 ) / prod( 34:52 )
pF = pA1CA2C * ( 4 / 33 )
pEF = (1/32) * (3/33) * pA1CA2C