Probability Definitions
Probability where each outcome is equally likely
What is Classical (Theoretical) Probability
What is the probability of rolling a number less than 4 on a 12 sided die?
What is 3/12 or 1/4
The number of ways 2 captains can be chosen from 13 players on a basketball team
What is Combination
According to a survey, 86% of adults in the U.S. think the government system is broken. Of those 86%, 8 out of 10 believe the government can be fixed. What is the probability that a randomly selected adult think that the government is broken and can be fixed?
0.86 x 0.80 = 0.688 or 68.8%
16P2
16!/(16-2)! = 240
Probability based on observations obtained from probability experiments (frequency of an event divided by total frequency)
What is Emperical (or statistical) probability
81% of households in the U.S. have computers. Of those households that have computers, 92% have internet access. What is the probability that a U.S. household selected at random has a computer and internet access?
0.81 x 0.92 = 0.745 or 74.5%
The number of ways 8 cars can line up in a row for a car wash
What is Permutation
According to a survey, 86% of adults in the U.S. think the government system is broken. Of those 86%, 8 out of 10 believe the government can be fixed. Given that a randomly selected adult thinks the government system is broken, what is the probability that he or she thinks the government cannot be fixed?
0.20 or 20%
8C3
(8!)/[(8-3)!(3!)] = 56
Set of all outcomes in a sample space that is not included in event E. Sometimes referred to as "E prime"
What is the complement of event E
The probability of a person in the U.S. has type A+ blood is 32%. What is the probability of 3 unrelated people in the U.S. all having type A+ blood?
0.32 * 0.32 * 0.32 = 0.0328 or 3.28%
The number of ways a 3 person committee can be chosen from 50 students
According to a survey, 86% of adults in the U.S. think the government system is broken. Of those 86%, 8 out of 10 believe the government can be fixed. What is the probability of selecting a random adult that believes the government is broken and cannot be fixed?
0.86 * 0.20 = 0.172 or 17.2%
How many different ways can the letters A, B, C, D, E, and F be arranged to form a 6 letter password?
6! = 720
Probability of an event occurring, given that another event has already occurred
What is conditional probability
You roll a 6-sided die. What is the probability of rolling 5 or a number greater than 3
1/6 + 3/6 = 4/6 = 0.67 or 67%
The number of 4 letter passwords that can be created when no letter can be repeated
Permutation
A multiple choice quiz has 5 questions each with four answer choices. Only one of the choices is correct for each question. You have no idea what the answer to any question and have to guess the answers. What is the probability that you answer the first 2 questions correctly?
1/25 * 1/25 = 0.0625 or 6.25%
A restaurant offers a dinner special that has 12 choices for entrees, 10 choices for side dishes, and 6 choices for dessert. For the special, you can choose one entree, two side dishes, and one dessert. How many different meals are possible?
Entree combinations = 12
Side dish combinations = 10!/(8!*2!)= 45
Dessert combinations = 6
Total Meals = 12*45*6 = 3,240
If events A and B cannot occur at the same time, events A and B are considered........
What is mutually exclusive
The starting lineup for a softball team consists of 9 players. How many different batting orders are possible using the 9 players that start?
The number of ways 24 different video games can be arranged side by side on a shelf
What is a permutation
A multiple choice quiz has 5 questions each with four answer choices. Only one of the choices is correct for each question. You have no idea what the answer to any question and have to guess the answers. What is the probability of answering none of the questions correctly
3/4 * 3/4 *3/4 *3/4 *3/4 = 3/4^5 = 0.237 or 23.7%
Given the letters "r e e t r a t". Find the number of distinguishable ways the letters can be arranged.
7!/(2!*2!*2!*1!) = 630