Section 4.6
Mathematical
Expectation
and Odds
Warm up
Mathematical Expectation
It
is the expected
monetary value of an
event.
ME = $ ∙ p($)
1)



Mulvihill is bidding on a landscaping job so
he can make some money for senior week.
The profit for the Alapocas job should be
about $3200 for the year with a probability
of 0.87. The profit of the Hockessin job will
be $3000 with a probability of 0.91.
However, with the costs of running the
landscaping he will lose $700 on equipment
repairs with a probability of 0.39.
What is his expected return for
each job?
2)




Janavel made up a new game
using one die.
If someone rolls an even
number, they win $2.
If they roll a one, they win $5.
If they roll a 3 or a 5, they pay
$4.
It costs $2 to play. What is the
mathematical expectation?
ODDS
 Odds
in favor
Formula:
p to q
p = want, q = don’t want
 Odds against
Formula:
q to p
p = want, q = don’t want
SHUT UP!

The probability of Mrs. Godfrey telling the
students to “Shut it” is 87%.
– What are the odds in favor of her screaming
“Shut it”?
– What are the odds against her screaming
“Shut it”?
World Series

The Yankees have a ⅛ chance of winning the
the World Series.
– What are the odds in favor of them
winning?
– What are the odds against them losing?
Deal or No Deal

In the Game Show Deal or No Deal, a
contestant begins by choosing 1 of 26
numbered cases. Each case holds a
different amount. Neither the host or the
banker, who offers to buy the contestant’s
case after each round, know what any
case contains.
What is the probability that you choose
the $1,000,000 case to begin with?
 If you played the game many, many times,
what is the expected value of the
amount that your case contains?
 Worksheet

Play as a Class

Record the following information in the
table.