Probability of Simple Events — Drills
Probability of Simple Events has 7 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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).
Basic
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A bag holds 6 red, 7 blue and 6 green marbles. Find P(red).
Worked answer
6/19
Total: 6 + 7 + 6 = 19
P = 619
Problem 2
A bag holds 8 red, 6 blue and 2 green marbles. Find P(green).
Worked answer
1/8
Total: 8 + 6 + 2 = 16
P = 18
Complement
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A bag holds 8 red, 5 blue and 3 green marbles. Find P(not blue).
Worked answer
11/16
Total: 16
Not blue: 8 + 3 = 11
1116 — or 1 - 516, the same thing.
Problem 2
A bag holds 2 red, 4 blue and 7 green marbles. Find P(not blue).
Worked answer
9/13
Total: 13
Not blue: 2 + 7 = 9
913 — or 1 - 413, the same thing.
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A spinner has 18 equal sections and P(win) = 13. How many sections win?
Worked answer
6
w18 = 13
w = 18 ÷ 3 = 6
Problem 2
A spinner has 16 equal sections and P(win) = 14. How many sections win?
Worked answer
4
w16 = 14
w = 16 ÷ 4 = 4
Samplespace
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Three fair coins are flipped. Find P(exactly one head).
Worked answer
3/8
Total outcomes: 23 = 8
Ways to get exactly one head: 3
38
Problem 2
Four fair coins are flipped. Find P(exactly one head).
Worked answer
1/4
Total outcomes: 24 = 16
Ways to get exactly one head: 4
14
Experimental
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A spinner is spun 20 times and lands on red 5 times. What is the experimental probability of red, as a decimal?
Worked answer
0.25
14 = 0.25
Problem 2
A spinner is spun 60 times and lands on red 12 times. What is the experimental probability of red, as a decimal?
Worked answer
0.2
15 = 0.2
Counting
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A number from 1 to 36 is chosen at random. Find P(multiple of 5).
Worked answer
7/36
Multiples of 5 up to 36: 7 of them
736
Problem 2
A number from 1 to 40 is chosen at random. Find P(multiple of 4).
Worked answer
1/4
Multiples of 4 up to 40: 10 of them
14
Area
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A spinner is half red, and 18 of it is blue. The rest is split evenly between 4 other colours. Find the probability of landing on one particular one of those colours.
Worked answer
3/32
Red and blue: 12 + 18 = 58
That leaves 1 - 58 = 38
Split 4 ways: 38 ÷ 4 = 332
Problem 2
A spinner is half red, and 13 of it is blue. The rest is split evenly between 3 other colours. Find the probability of landing on one particular one of those colours.
Worked answer
1/18
Red and blue: 12 + 13 = 56
That leaves 1 - 56 = 16
Split 3 ways: 16 ÷ 3 = 118