Theoretical vs Experimental
What kind of probability is calculated using known possible outcomes?
Theoretical Probability
Are rolling two dice considered independent or dependent events?
Independent
What tool helps list all possible outcomes in a structured visual format?
Probability Tree
What is the probability of rolling a 6 on a standard die?
1/6
You flip a coin and roll a 6-sided die. What is the probability of getting heads and a 4?
1/2 × 1/6 = 1/12
What type of probability is based on actual results from an experiment?
Experimental Probability
Drawing a card from a deck, not replacing it, then drawing another: independent or dependent?
Dependent
How many outcomes are possible when flipping two coins?
4 outcomes (HH, HT, TH, TT)
What is the probability of drawing a heart from a standard deck of cards?
13/52 = 1/4 or 25%
jar contains 5 red and 5 blue marbles. If you draw one marble, replace it, and draw again, what is the probability of getting two red marbles?
(5/10) × (5/10) = 1/4
If you roll a die 60 times and get a 4 fifteen times, what is the experimental probability of rolling a 4?
15/60 = 1/4 or 25%
Define independent events.
Events where the outcome of one does not affect the outcome of the other
Draw a simple tree diagram for flipping a coin and then rolling a 4-sided die. How many outcomes are there?
2 x 4 = 8
A spinner has 4 equal sections: red, blue, green, yellow. What is the probability of not getting red?
3/4 or 75%
You draw two cards from a deck without replacing the first. What is the probability that both are aces?
(4/52) × (3/51) = 1/221
How can you increase the accuracy of experimental probability results?
Increase the sample size
Define dependent events and give an example.
Events where the outcome of one affects the outcome of the other (e.g., drawing two cards without replacement)
What is the total number of outcomes when choosing a drink (3 choices) and a sandwich (4 choices)?
3 × 4 = 12 outcomes
A box contains 2 red, 3 blue, and 5 green balls. What is the probability of picking a blue one?
3/10 or 30%
A survey shows 80% of students like pizza and 70% like burgers. Assuming independence, what is the probability a student likes both?
0.8 × 0.7 = 0.56 or 56%
A coin is flipped 100 times and lands on heads 43 times. What is the theoretical probability of landing on heads, and how does it compare to the experimental result?
Theoretical = 1/2 or 50%, Experimental = 43/100 = 43%
You draw two marbles from a bag without replacing the first. What is the probability of drawing two red marbles if the bag contains 3 red, 2 blue, and 5 green marbles?
(3/10) × (2/9) = 6/90 = 1/15
Use an outcome table to determine the probability of getting a sum of 7 when rolling two dice.
6 outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so 6/36 = 1/6
A locker combination has 3 digits, each from 0–9. What is the probability of guessing the exact combination on the first try?
1/1000 (since 10 × 10 × 10 = 1000)
You spin a spinner with 3 equal sections (A, B, C), roll a die, and draw a card from a 52-card deck. What is the probability of landing on B, rolling a number greater than 3, and drawing a red card?
(1/3) × (3/6) × 263/52) = 1/3 × 3/6 × 1/2 = 1/12