Find Expected Value Lesson 6.5 Page 355 (Day 2)

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Find Expected Value Lesson 6.5Page 355(Day 2)
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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 x1 x2 x3 ...
P(Xi)
P(Xi)Xi
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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.
•  
• How much total money will the raffle earn after
  prizes are awarded if tickets are priced at
• 1 each?
•  2 each?
•  
•  
• What is the probability of a random ticket holder
  winning
• First prize, 1000?
• Second prize, 100?
• Third prize, 20?
• No prize, 0?

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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.
•  
•  
•  
• What is the probability of a random ticket holder
  winning more than 20?
•  
• What is the probability of a random ticket holder
  winning at least 20?
•  
• What is the probability of a random ticket holder
  winning less than 1000?
•  

X 0 20 100 1000
P(X)
XP(X)
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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.
• Whats the expected value, E, from your point of
  view?

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Homework Assignment

• Page 357 4, 5, and 6

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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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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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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.