Probability Review

Theoretical Probability

100

What is the formula for theoretical probability?

number of ways an event can occur / total number of outcomes

200

If you flip 3 coins, what is the probability that you get at least one heads?

P(at least one heads) = 7/8

300

Probability of rolling a 5 and a 6 on two dice.

P(5 and 6) = 1/36

400

Probability of rolling a 5 or a 6 on two dice.

P(5 or 6) = 20/36 = 5/9

500

Probability of one tail when flipping a coin 8 times.

P(1 T) = 8/256 = 1/32

Independent or Dependent?

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

200

Two events are dependent if ...

The probability of the second event is effected by the first event occurring.

300

Flipping a coin twice - independent or dependent?

Independent

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

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

Counting Principle

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

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

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

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

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

Expected Value

100

Generally describe how you find Expected Value.

Multiply each possible outcome by its probability, and then add all of the products together.

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

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...

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

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

Famous Years

100

The year Neil Armstrong walked on the Moon.

1969

200

The year World War II ended.

1945

300

The year Ann Arbor was founded.

1824

400

The year Michigan last won the NCAA Football National Championship.

1998

500

The year LeBron James was born.

1984