Expected Value

1
Expected Value

• MM1D2d Use expected value to predict outcomes

2
Expected Value

• The expected Value of the collection of outcomes
  is the sum of the products of the events
  probabilities and their values
• BASICALLY
• E event A value (prob. of event) event B
  value (Prob. of event)

3
Find the Expected Value

• EXAMPLE 1
• Consider a game in which two players each flip a
  coin. If both coins land heads up, then player A
  scores 3 points and player B loses 1 point. Find
  the expected value of the game for each player.

4
Consider a game in which two players each flip a
coin. If both coins land heads up, then player A
scores 3 points and player B loses 1 point. Find
the expected value of the game for each player.

• E event A value (prob. of event) event B
  value (Prob. of event)
• TT
• TH
• HT
• HH
• E 3(1/4) -1(3/4)
• E ¾ - ¾
• E 0

5
Expected Value

• Amanda has injured her leg and may not be able to
  play in next basketball game.
• If she can play the coach estimates the team
  will score 68 points.
• If she cannot play, the coach estimates the team
  will score 54 points.
• Determine the expected of points the team scores

6
Ex2

• E event A value (prob. of event) event B
  value (Prob. of event)
• E 68(.50) 54(.50)
• E 34 27
• E 61 points

7
Ex3

• A landscaper mows 25 lawns per day on sunny days
  and 15 lawns per day on cloudy days.
• 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

8
Ex3

• E event A value (prob. of event) event B
  value (Prob. of event)
• E 25(.65) 15(.35)
• E 16.25 5.25
• E 21.5 lawns per day