Permutations, Combinations, Counting Principle
What is the difference between permutations and combinations.
Permutations = order matters
Combinations = order does not matter
You draw a card from a standard deck of cards. You are now going to draw a second card. Describe what would make this an independent event?
Replacing the original card
According to a local college, the probability than an incoming Freshman will graduate in five years is 72%. What is the probability that they will NOT graduate in 5 years?
28%
Two urns both contain red balls and white balls. Urn 1 contains 5 red balls and 7 white balls and Urn 2 contains 9 red balls and 3 white balls. A ball is drawn from each urn. What is the probability that both balls drawn are white?
7/48
If an ice cream shop offers 31 flavors, 10 toppings, and 3 syrups, how many different ways can you make an ice cream choosing only 1 at a time?
930
A fair die is rolled and a spinner with numbers 1-4 is spun. How many possible outcomes are in the sample space?
24
Given the set U={1,3,5,7,9,11,13,15} if A=multiples of 3 and B=multiples of 5, what is A U B?
{3,5,9,15}
Let n be a random integer from 1 to 60. What is the probability that n is even given that it is greater than 20?
1/2
You are taking a matching test with 7 options for questions 1-4. You want to know how many different ways you can answer the four questions.
840
Suppose you pick one card from a standard deck of cards. What is the probability of drawing a card that is red and a multiple of 5.
4/52 = 1/13
Given the set U={1,3,5,7,9,11,13,15} if A=multiples of 3 and B=multiples of 5, what is (A n B)'.
{1,3,5,7,9,11,13}
Elena chooses one of the 30 tiles number 1 to 30. Let event A be the event that the number is odd and let event B be that number is a multiple of 3. Find P(B|A).
1/3
The school's debate team is made up of 12 seniors, 9 juniors, and 8 sophomores. A group of 9 will be chosen to perform at the state competition. How many ways are there to select 3 members from each grade level?
1,034,880
A bag contains 12 baseball cards and 8 superhero cards. An experiment consists of taking one card out of the bag, replacing it, and then selecting another card. What is the probability of selecting two superhero cards?
4/25
In the math classes at a school, 512 students took the summer review course. Of those students, 341 of them got an A. Of the 171 students who did not take the review course, 28 got an A. How many total students did not get an A.
314
The two-way data table shows data on the students at the college. Use the additional rule of probability to find the probability that a randomly selected student is a sophomore (Event A) or female (Event B). P(A U B).
67.7%
The school's debate team is made up of 12 seniors, 9 juniors, and 8 sophomores. A group of 9 will be chosen to perform at the state competition. Is this a permutation or a combination and what is the probability that the group does not have any sophomores.
.0293489619 or 29.3%
Hap is trying to find a matching pair of socks. He has 12 white socks,3 black socks, and 14 blue socks in the dryer and he will draw one sock at a time. What is the probability he will draw a white sock and then a black sock?
9/203
In a survey of 500 people, 260 prefer chicken and lemonade, 190 people in total prefer steak, and of the 90 people who prefer soda, 50 prefer chicken. Determine if liking chicken is independent of liking lemonade and how do you know?
P(C|L) does not equal P(C) hence they are dependent.
The students at a certain high school are 51% males. Of the students at the school, 45%of the males and 40% of the females say they regularly attend concerts. Find the probability that a student is a female and does not attend concerts.
29.4%