1.03 Review (Final AFM part 5)

Name:____________________________________________ Date_________ Period____ A#___
AFM Final Exam Review: Part 5 (Standard 1.03 – Probability)
I can statements:
I can use theoretical and experimental probability to model and solve problems.
□ I can use the addition and multiplication rules of probability.
□ I can calculate permutations and combinations and apply them in context.
□ I can create and use simulations for probability models.
□ I can find expected values and determine fairness of games.
□ I can identify and use discrete random variables to solve problems.
□ I can apply the binomial theorem to probability distributions.
Notes and Important Concepts:
Multiplication and Addition Rule of Probability:
□ 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) × 𝑃(𝐵) if the events are independent.

If I throw a die and then throw a second die, are those events independent? Why or
Why not?

What is the probability of rolling a 2 and then doubles with those two dice?

What is the probability of drawing a king, returning it to the deck, and then drawing a
heart?
□ 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)

What is the probability of rolling doubles or rolling a sum of 6 with two dice?

What is the probability of drawing a king or drawing a spade?

What is the probability of rolling a 2 and then a 3 or a 5 and then a 6?
□ The Fundamental Counting Principal, Permutations, and Combinations:
The Fundamental counting principal:

How many 5 character license plates are possible if all letters and number are allowed
with repetition?

How many 5 character license plates are possible if all letters and numbers are allowed
without repetition?

How many ways are there to select a 3 person committee from a group of 10 people?
□ Binomial Probability Distribution (combines combinations with multiplication rule of probability)

If the probability of a German Tank malfunctioning is .20, then what is the probability
that in a battalion of 20 tanks, 3 will malfunction?
□ Expected Value and Fair Games:
Is it fair? Find the expected value!
GAME: I’LL FLIP YOU FOR IT.
Version One: Two players decide who will be player 1 and player 2. Using two pennies and a nickel they will flip all
three coins at the same time. Player 2 scores a point if both pennies show heads or the nickel shows heads or both.
Player 1 scores a point if any or all of the coins show a tail. The winner is the player with more points at the end of
20 rounds.
Probability Player 1 wins:
Expected value for Player 1:
Probability Player 2 wins:
Expected Value for Player 2:
Is the game fair? Yes or No If no, how will you assign points to make it fair?
Version Two: Two players decide who will be player 1 and player 2. Using three pennies and one nickel they will flip
all four coins at the same time. Player 1 scores a point if all 3 pennies show heads or the nickel shows heads or
both. Player 2 scores a point if any or all of the coins show a tail. The winner is the player with more points at the
end of 20 rounds.
Probability Player 1 wins:
Expected value for Player 1:
Probability Player 2 wins:
Expected Value for Player 2:
Is the game fair? Yes or No If no, how will you assign points to make it fair?
□
All Probability Distributions sum to 1!
The probability that a store will sell x pairs of sneakers in a day is shown in the table below:
What’s
What’s
What’s
How
work
x
41
42
43
44
45
46
47
48
P(x)
.03
.10
.15
.17
.25
.15
.05
P(44)?
true about the sum of the P(x) column?
P(47)?
many pairs of sneakers can the store expect to sell? Think back to our
on expected value.
Practice: