Permutations & Combinations
You have 6 different books. How many ways can you arrange all of them on a single shelf?
720
(6!)
A bag contains 4 red, 5 blue, and 3 green marbles. What is the probability of drawing a blue marble?
5/12
A card is drawn from a standard deck. What is the probability that the card is a 7 or a Diamond?
16/52 or 4/13
A single die is rolled. What is the probability the result is a 6, given that the result is an even number?
1/3
p = 1-q
From a group of 10 students, how many ways can a committee of 3 be chosen?
120
(C(10,3))
A single die is rolled. What is the probability of NOT rolling a 2?
5/6
You flip a coin and roll a die. What is the probability you get Heads and a 5?
1/12
(1/2 * 1/6)
In a class, 50% are freshmen and 20% are freshmen who are also business majors. What is the probability that a randomly selected freshman is a business major?
0.4 or 40%
(0.2 / 0.5)
If my probability of failure is 0.16, what is p?
p = 0.84 or 84%
In how many distinct ways can the letters of the word UGLY be arranged?
24
(4!)
A classroom contains 4 freshmen, 3 sophomores, 8 juniors, and 8 seniors. What is the probability of choosing someone who isn't a junior?
15/23
What is the probability of rolling a 1 OR a 6 on a single die roll?
2/6 or 1/3
Two fair dice are rolled. Given their sum is 8, what is the probability at least one die shows a 3?
2/5
If p=0.32, what is my probability of failure?
0.68 or 68%
A committee of 4 people is to be formed from a group of 6 men and 7 women. How many committees can be formed if the committee must have exactly 2 men and 2 women?
315
(C(6,2) * C(7,2))
From a standard 52-card deck, what is the probability of drawing a card that is red and is also a face card (J, Q, K)?
6/52 or 3/26
At a university, 50% of students take a math class and 60% take an English class. If 30% of students take both, what is the probability that a randomly selected student takes math or English?
80% or 0.8
From a standard 52-card deck, this is the probability of drawing a King OR a Heart, given that the card drawn is a Face Card (a King, Queen, or Jack).
1/2
Carson had 45 shots on goal last season, but only made 22 of them. What is p (his probability of success)?
22/45 or 0.49 or 49%
How many combinations of dishes can I make if I have 12 options and only room for 7 of them on the menu?
792
You roll two standard six-sided dice. What is the probability that the sum of the numbers rolled is less than 5?
6/36 or 1/6
What is the probability of drawing a King OR a Club from a standard deck of 52 cards?
16/52 or 4/13
At a university, 20% of all students are in the College of Science and live on-campus. 40% of all students are in the College of Arts and live on-campus. These are the only two colleges at the university. What is the probability that a randomly selected student who lives on-campus is in the College of Science.
1/3
0.20/(0.20+0.40)
Lucy made it to 29 of her 48 lectures for college last semester. What is q?
19/48 or 0.4 or 40%