Expected Value
MM1D2d: Use expected value to
predict outcomes
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)
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.
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
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
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
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
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