Transcript EXPECTED VALUE (Day 2)

Find Expected Value
Lesson 6.5
Page 355
(Day 2)
EXPECTED VALUE (Day 2)
Definition:
The expected value (E) or mean of a random
variable is the sum of the probability of each
possible outcome of the experiment multiplied by
the value of that outcome.
E = P(x1)·x1 + P(x2)·x2 + P(x3)·x3 +... + P(xn)·xn
X
P(Xi)
P(Xi)·Xi
x1
x2
x3
...
EXPECTED VALUE (Day 2)
Warm-Up
A raffle is held. There are 5000 tickets sold. The single first prize ticket
is worth $1000. There are two second prize tickets worth $100. There
are five third prize tickets worth $20.
1. How much total money will the raffle earn after prizes are awarded if tickets are
priced at:
a. $1 each?
b. $2 each?
2. What is the probability of a random ticket holder winning:
a. First prize, $1000?
b. Second prize, $100?
c. Third prize, $20?
d. No prize, $0?
EXPECTED VALUE (Day 2)
Let X represent the amount of dollars won by a random ticket holder.
The possible values of X are $0, $20, $100, and $1000. Complete the
following probability table.
X
$0
$20
$100
P(X)
X·P(X)
3.What is the probability of a random ticket holder winning more than $20?
4.What is the probability of a random ticket holder winning at least $20?
5.What is the probability of a random ticket holder winning less than $1000?
$1000
EXPECTED VALUE (Day 2)
Coin Tossing Activity:
You & a friend each flip a coin. If both coins are heads, then your
friend scores 5 pts and you lose 2 pts. If both coins are tails, then
your friend loses 2 pts and you score 5 pts. If the coins land heads &
tails or tails & heads, you both score 1 pt.
Flip the coins 20 times and determine your scores.
What’s the expected value, E, from your point of view?
Homework Assignment:
Page 357 # 4, 5, and 6
4. Basketball
• Amanda has injured her leg and may not be able
to play in the next basketball game. If she can
play, the coach estimates the team will score 68
points. If she is not able to play, the coach
estimates the team will score 54 points. Her
doctor states there is a 50% chance she will be
able to play and a 50% chance she will not be
able to play. Determine the expected number of
points the team scores.
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Data Analysis & Probability
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Expected Value
5. Lawn Mowing
• A landscaper mows 25 lawns per day on
sunny days and 15 lawns per day on
cloudy days.
• If the weather is sunny 65% of the time
and cloudy 35% of the time, Find the
expected number of lawns the landscaper
mows per day.
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Data Analysis & Probability
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Expected Value
6. Seminar Attendance
• A hospital is holding a public seminar.
Officials estimate that 24 people will attend
if it does not rain and 16 people will attend
if it rains.
• The weather forecast indicates there is a
30% chance it will rain on the day of the
seminar.
• Find the expected number of people who
will attend the seminar.
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Data Analysis & Probability
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Expected Value