Definitions
What is the definition of Sample Space?
A list of all possible outcomes.
What is the sample space for flipping Quarter, twice?
{HH,HT,TH,TT}
What is the Probability that, when rolling a far die twice, you roll a 6 on the first roll and a 2 on the second roll?
Find P(6 and 2)
P(6 and 2) = (1/6)*(1/6) = 1/36 = 0.028
Two cards are selected, without replacement, from a standard deck of 52 cards. Find the probability that the second card is a queen, given that the first card is a king.
Find P(Q|K)
P(Q|K) = 4/51 = 0.078
The access code for a car's security system consists of four digits. Each digit can be the numbers 0 through 9. How many access codes if each digit can only be used once?
= 10 * 9 * 8 * 7 = 5040
OR
= 10P4 = 5040
What is the definition of a Permutation?
An ordered arrangement, where the order matters.
What is the Sample Space for Selecting a Calculator, at random, from Coach Raber's Calculator Bin in the Back of the Room?
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}
What is the probability of selecting a card from a deck that is a 4 or an ace?
Find P(4 or A)
P(4 or A) = (4/52) + (4/52) = 8/52 = 2/13 = 0.154
Find the probability that a child has a high IQ, given that the child has the gene.
Gene Gene Not
Present Present Total
High IQ 33 19 52
Normal IQ 39 11 50
Total 72 30 102
P(High IQ|Gene Present) = 33/72 = 11/24 = 0.458
How many ways can the word "MATH" be rearranged?
= 4! = 4 * 3 * 2 * 1 = 24 ways
What are Mutually Exclusive Events?
Events that can not occur at the same time.
What's the Probability of Rolling a number less than 5, on a fair die?
P(<5) = 4/6 = 2/3 = 0.67
A bag of marbles contains 6 red marbles, 4 blue marbles, 8 green marbles, and 5 yellow marbles. What is the probability that 3 red marbles are selected? (Without Replacement)
Find P(R,R,R)
P(R,R,R) = (6/23)*(5/22)*(4/21) = 120/10626 = 20/1771 = 0.011
High school students in one school chose their favorite leisure activity. Find the probability that when selecting one student, at random, they're favorite leisure activity is reading, given that they are male?
Sports Hiking Reading Other
Male 67 58 76 29
Female 39 48 85 39
P(R|M) = 76/230 = 38/115 = 0.330
A horse race has eight entries. Assuming that there are no ties, how many possible outcomes are there for 1st, 2nd, and 3rd place finishes?
= 8P3 = 336
What is the Definition of the Compliment of an Event?
*P(A) + P(A') = 1
What is he probability of selecting a person that is between 45 and 54 years old?
Age Frequency
15-24 54
25-34 366
35-44 233
45-54 180
55-64 125
65 and over 42
P(45-54) = 180/1000 = 9/50 = 0.180
In a sample of 500 students, there are 280 seniors. What is the probability of selecting 3 students where the first 2 are not seniors, if you can not select the same person more than once?
Find P(S',S',S)
P(S',S',S) = (220/500)*(219/499)*(280/498) = 0.109
A football game has an 80% chance of being canceled for a light drizzle and a 30% chance of being canceled for a heavy fog when there is no drizzle. There is a 70% chance of heavy fog and a 30% chance of a drizzle. What is the probability that the game will be canceled, given that there is heavy fog?
P(C|F) = (0.30)/(0.70) = 0.429
In a state lottery you must select 5 numbers out of 40 correctly to win the top prize, no matter the order. If you purchase a lottery ticket, what is the probability of winning the top prize? Leave answer in fraction form.
(HINT: Find the Total Number of Possible Outcomes First, then calculate Probability)
40C5 = 658008
P(W) = 1/658008
What is Subjective Probability?
Probability built from intuition, educated guesses, and estimates.
What's the probability of not choosing a 10 from a standard deck of cards?
P(10') = 1 - P(10) = 1 - (4/52) = 1/5 = 0.2
What is the probability of selecting a left handed male, or a right handed female?
Men Women Total
Left Handed 63 50 113
Right Handed 437 450 887
Total 500 500 1000
P(LM or RF) = (63/1000) + (450/1000) = 513/1000 = 0.513
The senior class is 55% female, and 32% are females who play a competitive sport. Find the probability that a student plays a competitive sport, given that the student is female.
P(S|F) = (0.32)/(0.55) = 0.582
A class has 30 students; 12 male, and 18 female. of the 12 males, 4 are in 11th grade and of the females, 8 of them are in the 11th grade. What is the total number of ways that we could select 4 students, at random, out of the class to participate in a survey?
=30C4 = 27405