Probability of Compound Events — Drills
Probability of Compound 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).
Counting
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A menu has 5 appetizers, 4 mains and 4 desserts. How many three-course meals are possible?
Worked answer
80
5 × 4 × 4 = 80
Problem 2
A menu has 6 appetizers, 3 mains and 3 desserts. How many three-course meals are possible?
Worked answer
54
6 × 3 × 3 = 54
Replacement
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A bag has 5 red and 5 blue marbles. Two are drawn WITHOUT replacement. Find P(both red).
Worked answer
2/9
First: 12
Second: 49 — one red gone, one marble gone
12 × 49 = 29
Problem 2
A bag has 6 red and 4 blue marbles. Two are drawn WITHOUT replacement. Find P(both red).
Worked answer
1/3
First: 35
Second: 59 — one red gone, one marble gone
35 × 59 = 13
Combinations
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
At a gathering of 5 people, everyone shakes hands with everyone else exactly once. How many handshakes?
Worked answer
10
5 × 4 = 20 ordered pairs
Each handshake was counted twice
20 ÷ 2 = 10
Problem 2
At a gathering of 8 people, everyone shakes hands with everyone else exactly once. How many handshakes?
Worked answer
28
8 × 7 = 56 ordered pairs
Each handshake was counted twice
56 ÷ 2 = 28
Independent
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
One spinner has 3 equal sections and another has 3. Find the probability that both land on section 1.
Worked answer
1/9
13 × 13 = 19
Problem 2
One spinner has 4 equal sections and another has 3. Find the probability that both land on section 1.
Worked answer
1/12
14 × 13 = 112
Dice
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two fair dice are rolled. Find P(sum = 11).
Worked answer
1/18
Pairs summing to 11: 2 of them
118
Problem 2
Two fair dice are rolled. Find P(sum = 3).
Worked answer
1/18
Pairs summing to 3: 2 of them
118
Complement
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Three fair dice are rolled. Find P(at least one 3).
Worked answer
91/216
P(not a 3 on one die) = 56
P(no 3 at all) = 125216
1 - 125216 = 91216
Problem 2
Two fair dice are rolled. Find P(at least one 3).
Worked answer
11/36
P(not a 3 on one die) = 56
P(no 3 at all) = 2536
1 - 2536 = 1136
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