Sample Space
Probability Basics
Likelihood
Compare Probabilities
Theoretical & Experimental Probability
Simulations & Law of Large Numbers
100
What is a sample space?
All of the possible outcomes!
100
What is probabillity?
The likelihood that an event will occur!
100
What word describes an event that has a 0% chance of happening?
Impossible.
100
How do you compare probabilities?
By converting them to the same format then determining which probability is more likely to happen (which one is closer to 1)!
100
What does "theoretical probability" mean?
The likelihood of an event occurring based on an IDEAL situation (NOT PROVEN)
100
What is a simulation in probability?
A Simulation is a way to estimate probabilities by using a computer to generate larger amounts of data or outcomes from a random process
200
What is the sample space of flipping a coin?
Heads and Tales
200
How do we write probability? Be specific!
200
If something has a 50% chance of happening, how likely is it?
Equally likely or as likely as not.
Neither likely nor unlikely
Equal chance.
200
Which is more likely: rolling a 3 or rolling a number greater than 4 on a number cube? Why?
Rolling a number greater than 4 because
2/6>1/6
200
What does "experimental probability" mean?
The likelihood of an event occurring based on ACTUAL outcomes (PROVEN)!
200
What is the Law of Large Numbers?
As the number of trials in an experiment increases, the experimental probability gets closer to the theoretical probability.
300
List the sample space for rolling a number cube (1–6).
1, 2, 3, 4, 5, and 6
300
Probability can be written 3 ways, but it must fall between what two specific numbers?
0 and 1!
300
You draw a card from a deck of 10 cards numbered 1 to 10. What is the likelihood of drawing a number less than 20?
Certain (because all numbers are less than 20)
300
A bag has 4 red, 3 blue, and 3 green marbles. Are you more likely to pull red or blue? Why?
Because there are more red marbles in the sample space.
Also, because
4/10>3/0
300
What is the theoretical probability of rolling a 3 on a die?
1/6
300
Why might a simulation give a slightly different result than the theoretical probability?
Because it’s based on chance and random outcomes, especially with fewer trials.
400
How many outcomes are in the sample space when you flip 2 coins?
four (2 heads and 2 tails)
400
What is the probability of rolling a 4 on a number cube?
1/6
400
A bag has 9 red marbles and 1 blue. What is the likelihood of drawing a blue one?
Unlikely.
400
True or False: P(rolling an odd number) = P(rolling an even number)?
True!
400
If you flip a coin 20 times and get 12 heads, what is the experimental probability of heads?
Simplify if you can!
12/20
3/5
400
You flip a coin 10 times and get 7 heads. Then you flip it 1,000 times and get about 500 heads. What concept does this demonstrate?
It shows the Law of Large Numbers—more trials lead to experimental results closer to the expected probability.
500
You randomly select a letter from the word “MATH.” What is the sample space?
M, A, T, H
500
die?A spinner has 4 equal sections: 1, 2, 3, and 4. What’s the probability of spinning a number greater than 2?
Simplify if you can!
2/4
Or
1/2
500
The chance of rain tomorrow is 0.25. How likely is that?
Unlikely.
500
Which is less likely: drawing a red card from 1 red and 9 black or drawing heads on a coin?
Drawing a red card because
1/10<1/2
1/10<5/10
500
A spinner has 3 equal colors. You spin it 15 times and get green 10 times. Is this experimental or theoretical?
Experimental!
500
You conduct a simulation of tossing 2 coins at once. After 200 trials, you get heads-heads 45 times. What is your experimental probability of heads-heads?
45/200
= 0.225 or 22.5%.
600
How many outcomes are in the sample space for a deck of cards? Why?
52 because there are 52 cards you can pick from
600
You draw a card from a deck with 5 red, 3 blue, and 2 green cards. What is P(blue)?
3/10
600
A team has a 0.85 probability of winning. How likely are they to win?
Likely.
600
A die has faces 1–6. Which is more likely: rolling 5 or not rolling 5? Explain.
Not rolling a five because
1/6<5/6
600
What is the theoretical probability of heads on a coin? Why might it not match experimental results?
The theoretical probability is 1/2 . This might not match experimental results because you cannot guarantee getting heads when you flip it (variation)!
600
If a student spins a spinner with 4 equal sections only 5 times and gets red 3 times, should they assume the probability of red is 3/5? Why or why not?
No, because with only a few trials, the results can be inaccurate. More trials are needed for reliable results, according to the Law of Large Numbers.