Combinatorics
If a lock has 5 digits, each from 0 to 9, how many different combinations are possible?
In a fair six-sided die, what is the probability of rolling a 3?
1/6
If you roll a fair six-sided die 100 times and it lands on 6 twenty times, what is the experimental probability of rolling a 6?
20%
If the probability of it raining on a given day is 0.3, and the probability of having a picnic on a rainy day is 0.1, what is the probability of having a picnic given that it's raining?
1/3
Probability
A measure of the likelihood of an event occurring, typically represented as a number between 0 and 1.
In how many ways can a committee of 3 people be selected from a group of 7?
35
If you flip a fair coin, what is the probability of getting heads?
1/2
In an experiment, a spinner with equal sections labeled 1 through 8 is spun 50 times, and it lands on 5 twenty-five times. What is the experimental probability of landing on 5?
25%
In a deck of cards, if you know that the drawn card is a spade, what is the probability that it's a face card (jack, queen, or king)?
3/13
Discrete Probability Distribution
A probability distribution where the random variable can only take on distinct, separate values.
How many different ways can 5 books be arranged on a shelf?
5!
What is the probability of randomly selecting a vowel (a, e, i, o, u) from the English alphabet?
5/26
If you flip a coin 200 times and it lands on tails 80 times, what is the experimental probability of getting tails?
80/200
If the probability of a student passing a math test is 0.8, and the probability of passing given that the student studied is 0.9, what is the probability that the student studied given that they passed?
.9
Continuous Probability Distribution
A probability distribution where the random variable can take on any value within a given range.
How many different arrangements are possible for the letters in the word "BANANA"?
Answer: 6!/3!=60(since there are three "A"s)
If you draw a card from a standard deck of playing cards, what is the probability of drawing a face card (jack, queen, or king)?
12/52=3/13 (since there are 3 face cards of each suit out of 52 cards)
A bag contains 30 marbles, 10 of which are red. If you randomly select 20 marbles with replacement and 6 of them are red, what is the experimental probability of selecting a red marble?
If the probability of selecting a green marble from a bag is 0.4, and the probability of selecting a green marble given that the first marble drawn was green is 0.6, what is the probability that the first marble drawn was green?
.4
Mutually Exclusive Events
Events that cannot occur at the same time.
If a license plate consists of 3 letters followed by 3 digits, how many different license plates are possible if repetitions are not allowed?
26^3×10^3=17,576,000
If you roll a fair ten-sided die, what is the probability of rolling a prime number?
4/10=2/5
If you toss a biased coin 50 times and it lands on heads 30 times, what is the experimental probability of getting heads?
30/50=.6
If you know that the probability of getting a red light while driving to work is 0.2, and the probability of being late to work given that you encounter a red light is 0.6, what is the probability of being late to work?
.12
Expected Value
The long-term average outcome of a random process, weighted by its probabilities.