Theoretical Probability
Independent or Dependent?
Counting Principle
Expected Value
Famous Years
100
What is the formula for theoretical probability?
number of ways an event can occur / total number of outcomes
100
If two events are independent, what do you do with their individual probabilities to find the probability that they happen together?
Multiply the individual probabilities
100
If there are m ways to choose one thing, and n ways to choose a second thing, then there are ____ ways to choose the two items together.
m x n
100
Generally describe how you find Expected Value.
Multiply each possible outcome by its probability, and then add all of the products together.
100
The year Neil Armstrong walked on the Moon.
1969
200
If you flip 3 coins, what is the probability that you get at least one heads?
P(at least one heads) = 7/8
200
Two events are dependent if ...
The probability of the second event is effected by the first event occurring.
200
For lunch you can choose between a PB+J, Ham, Turkey, Salami, or Fish sandwhich, and then a side of Regular, BBQ, Salt + Vinegar, or Baked Chips, and a drink of pop, water, gatorade, iced tea, or a milkshake. How many lunches are possible?
5 x 4 x 5 = 100
200
What is the Expected Value when rolling a die?
1 x 1/6 + 2 x 1/6 + 3 x 1/6 + 4 x 1/6 + 5 x 1/6 + 6 x 1/6 = 3.5
200
The year World War II ended.
1945
300
Probability of rolling a 5 and a 6 on two dice.
P(5 and 6) = 1/36
300
Flipping a coin twice - independent or dependent?
Independent
300
Tappan has 256 7th Grade students. If we wanted to pick a President and Vice-President for the 7th Grade from these 256 students, how many different combinations of students are possible?
256 x 255 = 65,280
300
The probability of winning a game is 1/12. If you win, you earn $18, and if you lose you have to pay $4. What is your expected value for this game?
18 x 1/12 + -4 x 11/12 = -2 and 1/6 or -2.1666...
300
The year Ann Arbor was founded.
1824
400
Probability of rolling a 5 or a 6 on two dice.
P(5 or 6) = 20/36 = 5/9
400
A bag has slips of paper inscribed with the numbers 1-10. To pick a two-digit number, a player selects one slip and then a second slip without replacement. What is the probability of selecting the number 98?
P(9 then 8) = 1/10 x 1/9 = 1/90
400
There are 5 main AAPS middle schools running Track (Tappan, Slauson, Scarlett, Forsythe, and Clague). How many different ways can the teams finish in the final standings (e.g. first team, second team, third team, fourth team, fifth team)?
5 x 4 x 3 x 2 x 1 = 120
400
For a 70% Free-Throw Shooter, what is their expected value for every one-and-one situation?
0 x 0.30 + 1 x 0.21 + 2 x 0.49 = 0.21 + 0.98 = 1.19 points
400
The year Michigan last won the NCAA Football National Championship.
1998
500
Probability of one tail when flipping a coin 8 times.
P(1 T) = 8/256 = 1/32
500
For the Daily 3 lotto game, a machine selects from balls numbered 0-9 for three separate slots. The numbered balls are combined to form a 3 digit number, and a player wins if their 3 digit number matches the generated number. What is the probability of winning the Daily 3 game?
1/1000
500
There are 14 teams in the Big-10 Football conference (including Michigan and Michigan State). How many ways can all 14 teams finish in the final standings, 1-14?
87,178,291,200
500
For a 70% Free-Throw Shooter, what is their expected value for a two free-throw situation?
0 x 0.09 + 1 x 0.42 + 2 x 0.49 = 0.42 + 0.98 = 1.4 points
500
The year LeBron James was born.
1984
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