Probability of Compound Events — Practice
Two or more things happening: multiply along a path, add across paths, and watch whether the first event changes the second.
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
Cam has 4 shirts and 3 pairs of pants. How many different outfits?
Worked answer
12
4 × 3 = 12
Problem 2
Two fair dice are rolled. How many outcomes are in the sample space?
Worked answer
36
6 × 6 = 36
Problem 3
Two fair coins are flipped. Find P(both heads).
Worked answer
1/4
12 × 12 = 14
Problem 4
A menu has 5 appetizers, 4 mains and 3 desserts. How many three-course meals?
Worked answer
60
5 × 4 × 3 = 60
Problem 5
A fair die is rolled twice. Find P(both sixes).
Worked answer
1/36
16 × 16 = 136
Problem 6
A bag has 4 red and 6 blue marbles. One is drawn, replaced, then another is drawn. Find P(both red).
Worked answer
4/25
P(red) = 410 each time
410 × 410 = 16100 = 425
Problem 7
Same bag (4 red, 6 blue), but the first marble is NOT replaced. Find P(both red).
Worked answer
2/15
First: 410
Second: 39 — one red gone, one marble gone
410 × 39 = 1290 = 215
Problem 8
Two fair dice are rolled. Find P(sum = 7).
Worked answer
1/6
Pairs summing to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — six of them
636 = 16
Problem 9
A spinner is red or blue, equally likely. A fair die is rolled. Find P(blue and an even number).
Worked answer
1/4
P(blue) = 12
P(even) = 12
12 × 12 = 14
Problem 10
Six people each shake hands with every other person exactly once. How many handshakes?
Worked answer
15
6 × 5 = 30 ordered pairs
Each handshake was counted twice
30 ÷ 2 = 15
Problem 11
How many different 2-person teams can be chosen from 7 students?
Worked answer
21
7 × 6 = 42 ordered pairs
42 ÷ 2 = 21
This is (72).
Problem 12
Two fair dice are rolled. Find P(at least one 6).
Worked answer
11/36
P(no six on one die) = 56
P(no six at all) = 56 × 56 = 2536
1 - 2536 = 1136
Problem 13
A box has 9 good and 3 defective parts. Two are drawn without replacement. Find P(both good).
Worked answer
6/11
First: 912
Second: 811
912 × 811 = 72132 = 611
Problem 14
In a league of 8 teams, each pair plays twice. How many games in total?
Worked answer
56
Pairs: 8 × 72 = 28
Each pair plays twice: 28 × 2 = 56
Problem 15
Three fair coins are flipped. Find P(exactly two heads).
Worked answer
3/8
The 8 outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
Exactly two heads: HHT, HTH, THH — three of them
38
Problem 16
A drawer has 5 white and 3 black socks. Two are pulled without replacement. Find P(one of each colour).
Worked answer
15/28
White then black: 58 × 37 = 1556
Black then white: 38 × 57 = 1556
Add the two paths: 3056 = 1528