Theoretical Probability
The theoretical probability of rolling a 3 on a fair number cube.
1/6
You flip a coin 10 times and get heads 4 times. This is the experimental probability of heads.
4/10, or 2/5?
A tree diagram shows all of these in a probability experiment
possible outcomes
You flip a coin and roll a number cube. This is how many total outcomes are possible.
12
You have 2 shirts and 3 pants. This is how many outfits you can make using the Counting Principle.
6
The theoretical probability of rolling an even number on a fair number cube.
3/6, or 1/2
A student spins a spinner 20 times and lands on green 5 times. This is the experimental probability of landing on green.
5/20, or 1/4
A tree diagram shows 2 choices for drinks and 3 choices for snacks. This is the total number of outcomes at the end of the tree.
6
(2 × 3)
You roll a number cube and flip a penny. This is the probability of rolling a 1 and getting tails
1/12
You have 3 sandwiches and 2 drinks. This is how many lunch combinations you can make.
6
On a number cube, this is the theoretical probability of rolling a number greater than 4.
2/6, or 1/3
A student flips a coin 30 times and gets heads 12 times. This is the experimental probability of landing on heads.
12/30, or 2/5
This vocabulary word means “the list of all possible outcomes of a probability experiment.”
sample space
You flip a coin twice. This is the probability of getting heads on both flips.
1/4
You have 3 shirts, 2 pants, and 2 jackets. This is how many outfits you can make using the Counting Principle.
12
A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. This is the theoretical probability of choosing a blue marble.
3/12, or 1/4
After 40 spins of a spinner, a student lands on yellow 18 times. This is the experimental probability of landing on yellow.
18/40, or 9/2
This statement correctly describes the difference between theoretical and experimental probability.
Theoretical probability is what should happen, and experimental probability is what actually happens
You roll a number cube and spin a spinner with 4 equal sections. This is the probability of rolling a 2 and landing on green
1/24
A cafeteria offers 4 sandwich options, 3 drinks, and 2 desserts. Using the Counting Principle, this is how many possible lunch combinations exist.
24
A bag has 3 red beads, 4 blue beads, 5 green beads, and 8 yellow beads. This is the theoretical probability of choosing a bead that is not yellow
12/20, or 3/5
During a game, a student rolls a number cube 60 times. The results show:
• 1: 8 times
• 2: 14 times
• 3: 6 times
• 4: 12 times
• 5: 10 times
• 6: 10 times
This is the experimental probability of rolling a 4 or 5.
22/60, or 11/30
A student says: “My experimental probability of landing on blue was 0.40, but the theoretical probability was 0.25.”
This color (blue) was landed on more or less often than expected?
more often
You flip a coin, draw one card from a bag with 3 red and 2 blue cards, and then roll a number cube. This is the probability of getting heads, then a red card, then rolling a 1 or 2.
(1/2) × (3/5) × (2/6) = 6/60, or 1/10
A student can choose from 4 shirts, 3 pants, 2 hats, and 5 pairs of shoes. Using the Counting Principle, this is how many total outfit combinations are possible.
120