Probability of Simple Events — Practice
Probability is a fraction: what you want over everything that could happen — as long as every outcome is equally likely.
What these questions cover
These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Sample space — The set of all possible outcomes.
- Complement — Everything except the event. P(not A) = 1 - P(A).
Problem 1
A fair 6-sided die is rolled. Find P(rolling a 5).
Worked answer
1/6
P = 16
Problem 2
A fair 6-sided die is rolled. Find P(even).
Worked answer
1/2
Even faces: 2, 4, 6 — that is 3 of them
36 = 12
Problem 3
A bag holds 3 red and 5 blue marbles. Find P(red).
Worked answer
3/8
3 + 5 = 8 marbles
P(red) = 38
Problem 4
For the same bag (3 red, 5 blue), find P(not red).
Worked answer
5/8
1 - 38 = 58
Same as counting the 5 blue marbles directly.
Problem 5
A spinner has 8 equal sections, 3 of them green. Find P(green).
Worked answer
3/8
P = 38
Problem 6
A bag holds 4 red, 6 blue and 10 green marbles. Find P(not blue).
Worked answer
7/10
Total: 4 + 6 + 10 = 20
Not blue: 4 + 10 = 14
1420 = 710
Problem 7
A spinner has 40 equal sections and P(win) = 15. How many sections are winners?
Worked answer
8
w40 = 15
w = 40 ÷ 5 = 8
Problem 8
A number from 1 to 20 is chosen at random. Find P(multiple of 3).
Worked answer
3/10
Multiples of 3 up to 20: 3, 6, 9, 12, 15, 18 — six of them
620 = 310
Problem 9
Two fair coins are flipped. Find P(exactly one head).
Worked answer
1/2
Sample space: HH, HT, TH, TT — four equally likely outcomes
Exactly one head: HT and TH, so two of them
24 = 12 — not 13, because "one of each" happens two ways.
Problem 10
A spinner is spun 60 times and lands on red 21 times. What is the experimental probability of red, as a decimal?
Worked answer
0.35
2160 = 0.35
Problem 11
If P(A) = 0.35, find P(not A).
Worked answer
0.65
1 - 0.35 = 0.65
Problem 12
A bag has only red and blue marbles, 30 in all, and P(red) = 25. How many are blue?
Worked answer
18
Red: 25 × 30 = 12
Blue: 30 - 12 = 18
Problem 13
Three fair coins are flipped. Find P(at least one head).
Worked answer
7/8
The opposite is no heads at all: TTT
There are 23 = 8 equally likely outcomes, so P(TTT) = 18
1 - 18 = 78
Problem 14
A number from 1 to 30 is chosen at random. Find P(multiple of 4 or 5).
Worked answer
2/5
Multiples of 4: 4, 8, 12, 16, 20, 24, 28 — seven
Multiples of 5: 5, 10, 15, 20, 25, 30 — six
20 is in both lists, so subtract it once: 7 + 6 - 1 = 12
1230 = 25
Problem 15
A bag has 5 red and 7 blue marbles. How many red marbles must be added so that P(red) = 12?
Worked answer
2
5 + x12 + x = 12
Cross-multiply: 10 + 2x = 12 + x
x = 2
Check: 7 red and 7 blue ✓
Problem 16
A spinner is half red and a quarter blue; the rest is split evenly between green and yellow. Find P(green).
Worked answer
1/8
Red and blue take 12 + 14 = 34
That leaves 14 for green and yellow
Split evenly: 14 ÷ 2 = 18