Probability Basics
A fair coin is flipped twice.
What is the probability of getting exactly one head?
1/2
Possible outcomes: HH, HT, TH, TT → 4 total outcomes
Exactly one head: HT, TH → 2 outcomes
Probability = 2 ÷ 4 = 1/2
A diagram made of circles showing how groups overlap.
a Venn diagram
This tool helps us calculate probability when groups share people or items.
a Venn diagram
The total number of possible outcomes.
the sample space
10 - 3.3
6.7
A fair six-sided die is rolled twice.
What is the probability of getting a total of 8?
5/36
• Possible pairs for total 8: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes
• Total possible outcomes = 6 × 6 = 36
• Probability = 5 ÷ 36 = 5/36
In a Venn diagram, this section shows people who are in both groups.
the intersection
You pull a name from a Venn diagram. It lands in both circles. What’s the probability
the number in the overlap divided by the total
What does “mutually exclusive” mean
events that cannot happen at the same time
If x = 5, what is the value of 3x + 2?
17
A bag contains 4 blue, 3 red, and 3 green counters. A counter is selected at random.
What is the probability that it is not green?
7/10
• Total counters = 4 + 3 + 3 = 10
• Not green = blue + red = 4 + 3 = 7
• Probability = 7 ÷ 10 = 7/10
How many parts are in a 2-circle Venn diagram?
4 (Group A only, Group B only, Both, Neither)
There are 20 students. 12 like maths, 9 like English, 5 like both. What’s the probability a student likes neither
20 – (12 + 9 – 5) = 4, so 4/20 or 1/5
What does the symbol ∪ mean
union (A or B)
How many degrees are in a right angle
90°
A back contains 80 blue marbles, 6 red marbles, 24 purple marbles.
What is the probability of picking a yellow marble?
0
If someone is not in either group, where do they go in the diagram?
outside the circles
From a Venn diagram, 6 students like dogs, 4 like cats, 2 like both. What’s the total number of students
6 + 4 – 2 = 8
What does the symbol ∩ mean
intersection (A and B)
What is 10% of $100,000
$10,000
A spinner numbered 1 to 8 is spun once.
What is the probability of getting a prime number?
1/2
Prime numbers between 1 and 8: 2, 3, 5, 7 → 4 numbers
Total numbers = 8
Probability = 4 ÷ 8 = 1/2
You place a person in only one circle. What does that mean
they belong to one group only (not both)
You’re told P(A) = 0.3, P(B) = 0.4, and P(A ∩ B) = 0.1. P(A ∪ B)
0.3 + 0.4 – 0.1 = 0.6
Explain the difference between theoretical and experimental probability.
: theoretical is based on maths, experimental is based on real trials
Solve X
3x+5=20
x = 5