Theoretical Probability
What is the probability of flipping tails on a fair coin?
1/2
A student flips a coin 40 times and gets 26 tails. What is the experimental probability of tails?
26/40 or 13/20
A class has 30 students; 12 prefer science. What is the relative frequency for science?
12/30 or 2/5
There is a 100% chance of snow. How do you describe this chance?
Certain
A round pool has a radius of 6 meters. What is its area?
About 113.04 m² (π × 6² = 3.14 × 36)
What is the probability of rolling a number less than 4 on a 6-sided die?
3/6 or 1/2
A die is rolled 50 times and lands on 5 a total of 12 times. What is the experimental probability of rolling a 5?
12/50 or 6/25
Sarah’s tile draws (60 total): Red=24, Yellow=18, Blue=18. Estimate how many red tiles are in a 120-tile bag.
48
A spinner has 3 red sections and 1 yellow section. Is it fair?
No, because red has more sections than yellow.
A circular track has a diameter of 10 meters. What is the circumference?
About 31.4 m (π × 10)
A student rolls two dice. What is the probability the sum is 7?
6/36 or 1/6
A spinner is spun 80 times and lands on blue 32 times. What is the experimental probability of blue?
32/80 or 2/5
Estimate the number of yellow tiles in the 120-tile bag.
36
A die has the number 6 on two faces. Is it fair? Explain.
No, because the probability of rolling a 6 is higher.
Find the volume of a rectangular prism 10 cm × 3 cm × 4 cm.
120 cm³
A spinner has 5 equal sections labeled W, X, Y, Z, and V. What is the probability of landing on Z?
1/5
Liam’s spinner results: P=8, Q=16, R=8, S=8. What is the experimental probability of landing on Q?
16/40 or 2/5
Which color is least likely to be drawn in Sarah’s tiles?
Yellow or Blue (tie at 18 each; either acceptable)
A spinner has 8 sections; one section is larger than the others. Is it fair?
No, because the larger section has a higher chance to be landed on.
Find the volume of a rectangular prism 6 m × 5 m × 2 m.
60 m³
A card is drawn from a standard deck of 52 cards. What is the theoretical probability of drawing a diamond?
13/52 or 1/4
Is Liam’s spinner fair? Why or why not?
No, because Q appears twice as often as other sections.
In 100 spins of Liam’s spinner, how many times would you expect to land on Q?
50 times (since Q is 2/5 probability)
A bag has 5 green, 3 purple, and 2 blue balls. Is it likely or unlikely to pick a purple ball?
Likely (3 out of 10 balls)
A cube has a volume of 64 cm³. What is the length of each side?
4 cm (because 4 × 4 × 4 = 64)