\magnification 2000
\parindent 0pt
\parskip 12pt
\pageno=1
\hsize 7.5truein
\hoffset -0.35truein
\voffset -0.3truein
\vsize 10truein
\def\u{\vskip -10pt}
\def\v{\vfill}
\def\s{\vskip -5pt}
\def\w{\vskip 20pt}


2.6 Finite probability

Suppose $E \subset S$, then the probability of $E$ = $P(E) = {|E| \over |S|}$

$S$ = sample space, $E$ = events.

Note:  we assume each outcome is equally likely


Ex: A football season consists of 11 games.  What is the probability that the season ends in 7 wins, 2 losses, and 2 ties, IF it is equally likely that the football team wins, looses, or ties.

The number of ways the season can end in 7 wins, 2 losses, and 2 ties is
\v

The number of different ways in which the season can end is
\v

Thus the probability that the season ends in 7 wins, 2 losses, and 2 ties is

\v


\eject

Suppose you randomly place 5  rooks on an $8 \times 8$ chessboard in nonattacking position.
Suppose 2 of the rooks are yellow and three are blue.  What is the probability that a yellow rook is in the first row and first column.

Number of ways to place 2 yellow rooks and 3 blue rooks on an $8 \times 8$
chessboard where a yellow rook is in the first row and first column =

\v\v\v



Number of ways to place 2 yellow rooks and 3 blue rooks on an $8 \times 8$
chessboard =



\v\v\v
\hrule



What is the probability that a yellow rook is in the first row and second column.



\end