Probability Basics
Addition Rule, Conditionals, and Complements
Multiplication Rule and Independent/Dependent Events
Counting Rules, Permutations, and Combinations
Distributions and Central Limit Theorem
100
How many samples are in the sample space when flipping a coin three times?
8
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
100
A candy jar contains 4 caramel, 5 cherry, and 7 chocolate candies. What is the probability of selecting a caramel or a chocolate candy?
Total = 16
P(caramel or chocolate) = (4+7)/16 = 11/16 = 0.688
100
What is the probability of flipping a head and rolling a 2 on a die?
P = (1/2) * (1/6) = 1/12
100
Is choosing 5 books to take on vacation from a stack of 10 a permutation or combination?
Combination (order doesn’t matter)
100
Is this a Discrete Probability Distribution?
Yes, x values are discrete and
sumP(x)=1
200
If you roll a fair die, what is the probability of rolling a 5?
P(5) = 1/6 = 0.167
200
What is the probability of not rolling a 2 on a standard die?
P(not 2)= 1 − 1/6 = 5/6 = 0.833
200
If the probability of surviving a year is 0.997, what is the probability that four randomly selected people all survive?
P = 0.997⁴ ≈ 0.988
200
A pin consists of 2 letters followed by 2 digits (0–9). How many different passwords are possible if duplicates are allowed?
26C1*26C1*10C1*10C1= 26^2 × 10² = 67,600
200
If 25% of people own electric cars, find the probability that in a group of 8 people, exactly 2 own electric cars.
Binomial: Success=own an electric car
p=0.25, q=0.75, n=8, x=2
P(2) =_8C_2 *(0.25)² *(0.75)⁶=0.311
300
What is the probability of drawing an ace from a standard deck of 52 cards?
P(Ace) = 4/52 = 1/13 = 0.0769
300
In a survey, 10 out of 30 people said “No” to a question. What is the probability someone did not say “No”?
P(not No) = 1 − 10/30 = 20/30 = 0.667
300
Reed loves going to the farmers market. Each week, he has an 18% chance of buying flowers, a 23% chance of buying apples, a 42% chance of buying a loaf of bread, and a 17% chance of buying tomatoes. Each decision is independent of his other decisions. What is the probability that Reed buys both flowers and bread?
- P(flowers and bread) = P(A) * P(B) = 0.18 * 0.42 = 0.0756
300
Is selecting a president and vice president a permutation or combination?
Permutation (order matters)
300
Find the mean for x:
µ = 0(0.1) + 1(0.6) + 2(0.3) = 1.2
400
In a game, you spin a spinner 250 times and land on blue 47 times. Find the empirical probability of landing on blue.
P(Blue) = 47/250 = 0.188
400
In a group of 9,200 people, 250 are smokers. Among the smokers, 30 developed a specific illness. Find P(Illness | Smoker).
P(Illness | Smoker) = 30/250 = 0.12
400
What is the probability of getting at least one head when tossing a coin 4 times?
P(at least one head)= 1 − (1/2)⁴ = 1 − 1/16 = 15/16
400
A pin consists of 2 letters followed by 2 digits (0–9). How many different passwords are possible if NO duplicates are allowed?
26C1*25C1*10C1*9C1=58,500
400
Compute the z-score for a normal distribution with x = 72, µ = 68, σ = 5.
z = (72−68)/5 = 0.8
500
Out of 60 people, 24 have blood type A. What is the probability of randomly selecting someone with blood type A?
P(Type A) = 24/60 = 0.40
500
In a study of 1,200 students, 300 snored and 180 of them liked to play video games. What is P(Video Games | Snores)?
P(Video Games|Snores)= 180/300 = 0.60
500
In a survey, it is found that 10 out of 13 people walk to the office. 3 persons are selected randomly. What is the probability that all three walk to the office?
These are dependent events: one influences the next by changing the sample size:
P(A and B) = P(A) · P(B|A)
The probability that all three walk to the office = (10/13) × (9/12) × (8/11) = 720/1716 = 0.4196
500
From 7 desserts, how many ways can you pick 3 if the order doesn’t matter?
7C3 = 35
500
The average daily revenue of a store is $1200 with a standard deviation of $300. For samples of size 16, what is the standard error?
16 days were chosen to check the average daily revenue. The more days sampled, the smaller the error
SE = 300/sqrt16=75