Transcript Advanced Math Topics

Advanced Math Topics
4.6 Mathematical Expectation and
Odds
Mathematical Expectation: The amount of money expected to be won or lost in an event
or series of events.
Mathematical Expectation Formula =
m1p1 + m2p2 + m3p3 + … + mnpn
The amount earned (or lost) if an event occurs times the probability of that event.
Note: If money will be lost when the event occurs, then m is negative.
1) If the it snows, a construction company will lose $40,000 on a project on HWY 80.
If it does not snow, the company will profit $200,000. There is a 28% chance of snow.
Find the mathematical expectation.
(.28)(-40,000) + (.72)(200,000) = $132,800
2) A street vendor is performing a gambling game for $10. You flip a coin, then roll a die.
If you flip a head and an even number you win your $10 back.
If you flip a tail and a 1 or 2, you win $30.
All other outcomes, you win $1.
1
Find your mathematical expectation and decide if you should play.
H
2
3
4
5
6
T
1
2
3
4
5
6
$10(3/12) + $30(2/12) + $1(7/12) = $8.08
It costs $10 to play and your expected return is $8.08.
You should not play.
If the charge were less than $8.08, then it would be
advantageous to play.
The number of unfavorable outcomes.
Odds in favor of an event =
p:q
The number of favorable outcomes.
3) You roll two dice. Find the odds in favor of rolling a sum of 6.
The ways to roll a sum of 6 are 1,5 ; 5,1 ; 2,4 ; 4, 2 ; and 3,3.
These are the 5 favorable outcomes.
There are 36 total outcomes.
Thus, there are 31 unfavorable outcomes.
5 : 31
4) Seniors make up 26% of the SRVHS student body. If the Student of the Month
is selected and has an equal chance of being from all 4 classes, what are the odds in
favor of the student being a senior.
There are 26 favorable outcomes for every 74 unfavorable outcomes.
26 : 74 = 13 : 37
5) The probability that the Staff Team wins the Dodge Ball Championship this year
Is 143/150. Find the odds in favor of the Staff Team winning.
There are the 143 favorable outcomes and 7 unfavorable outcomes.
143 : 7
6) The odds in favor in a horserace for “Cash” to win is 2:5 and 7:17 for “Princess”.
Who is the favorite, between the two, to win?
Cash has 2 favorable outcomes & 5 favorable outcomes. P(Cash winning) = 2/7 = .286.
Princess has 7 favorable outcomes & 17 favorable outcomes. P(Princess) = 7/24 = .292.
Can you increase your chances of winning the lottery by picking certain #’s?
No, lotteries are designed so that each person has equal chance of winning.
All numbers have an equal chance of being selected.
Can you decrease the possible players you split the jackpot with, if you win?
Yes, this can be done by not selecting numbers that people often select like
months of the year, birthdays, holidays, etc.. If you win by staying away
from these common selections, there will be a less chance of other people
who picked the same numbers as you, and you may not have to split the winnings.
Thus, the numbers 1-12 and 1-31 are selected more frequently than other numbers.
Staying away from these numbers may increase your winnings while the
probability of winning stays the same.
HW
• P. 224 #1-13 Skip #8,9
• Ch 4 Test on Thursday