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 event’s 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