Simple Events
What is the probability of rolling a 4 on a fair six-sided die?
1/6
What is a sample space? Give a short definition and one example
A sample space is the set of all possible outcomes of an experiment. Example: For one coin toss, sample space = {H, T}.
State the Fundamental Counting Principle in one short sentence
If one event can occur in m ways and a second independent event can occur in n ways, then both events together can occur in m×n ways.
A bag contains 3 red, 2 blue, and 5 green marbles. What is the probability of randomly drawing a blue marble?
1/5
Use a simple tree diagram or list to write the sample space for flipping one coin and rolling one 4-sided die (sides 1–4). How many outcomes are in the sample space?
Coin outcomes {H, T}. Die outcomes {1,2,3,4}. Sample space = {(H,1),(H,2),(H,3),(H,4),(T,1),(T,2),(T,3),(T,4)}. Number of outcomes = 2×4=8
If a sandwich shop offers 3 breads and 4 fillings, how many different one-bread-one-filling sandwiches are possible?
12
Explain in one sentence the difference between an impossible event and a certain event and give an example of each
An impossible event cannot happen (probability = 00). Example: rolling a 7 on a fair six-sided die. A certain event always happens (probability = 11). Example: when you roll a six-sided die, getting a number between 1 and 6.
Use a tree diagram or list to find the sample space for flipping two coins. List all outcomes and state how many outcomes show two tails.
Sample space = {HH, HT, TH, TT}. Outcomes showing two tails = {TT} — 1 outcome. Total outcomes = 4.
A student needs to choose one shirt (5 choices), one pair of pants (3 choices), and one pair of shoes (4 choices). Using the Fundamental Counting Principle, how many different outfits are possible?
60
A spinner has 8 equal sections numbered 1–8. What is the probability of spinning a number greater than 6?
2/8 or 1/4
A spinner has colors red and blue. A marble (from a bag) can be red, blue, or yellow. Draw the tree diagram outcomes for picking a marble then spinning the spinner; how many total outcomes are there?
6
A password is made of 2 letters (A–Z) followed by 2 digits (0–9). Assuming repetition is allowed, how many different passwords are possible?
67,600
Two coins are tossed. What is the probability of getting exactly one head? Show the sample space and give the probability.
{HH, HT, TH, TT} (4 outcomes). Exactly one head: {HT, TH} — 2 favorable outcomes. Probability = 2/4=1/2