Basic Probability
A bag contains 4 red, 5 blue, and 3 green marbles. What is the probability of drawing a blue marble?
5/12
A car model comes in 4 colors and 3 interior styles. How many different variations are possible?
12
You have 6 different books. How many ways can you arrange all of them on a single shelf?
720 (6!)
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
You flip a coin and roll a die. What is the probability you get Heads and a 5?
1/12 (1/2 * 1/6)
A single die is rolled. What is the probability of NOT rolling a 2?
5/6
How many 3-digit area codes are possible if the first digit cannot be 0 or 1?
800 (8 x 10 x 10)
From a group of 10 students, how many ways can a committee of 3 be chosen?
120 (C(10,3))
If P(A) = 0.4, P(B) = 0.2, and A and B are mutually exclusive, what is P(A or B)?
0.6
A single die is rolled. What is the probability the result is a 6, given that the result is an even number?
1/3
Two coins are flipped. What is the probability of getting at least one Head?
3/4
A quiz has 5 multiple-choice questions, and each question has 4 possible answers. How many ways are there to answer the quiz?
1024 (4^5)
In a race with 8 runners, how many different ways can the Gold, Silver, and Bronze medals be awarded?
336 (P(8,3))
What is the probability of rolling a 1 OR a 6 on a single die roll?
2/6 or 1/3
The probability of a flight being on time is 0.8. What is the probability that your next two (independent) flights are both on time?
0.64 (0.8 * 0.8)
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
A restaurant offers 4 appetizers, 6 main courses, and 3 desserts. How many different three-course meals are possible?
72 (4 x 6 x 3)
A team of 12 players needs to choose a captain and a co-captain. How many different ways can this be done?
132 (P(12,2))
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
A bag has 3 red and 7 blue marbles. You draw a marble, DON'T replace it, then draw another. What is the probability both are red?
6/90 or 1/15
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 (Sums of 2, 3, 4)
How many 4-digit PINs can be created if digits cannot be repeated?
5040 (10 x 9 x 8 x 7)
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))
What is the probability of drawing a King OR a Club from a standard deck of 52 cards?
16/52 or 4/13
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?
40% or 0.4 (0.2 / 0.5)