Probability Basics
A 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 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
A Venn diagram shows the names of 40 students. 6 of the names are in the intersection.
What is the probability you pick a name in the intersection?
Percentage Answer
= 15%
Probability = 6 ÷ 40 = 0.15 = 15%.
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 bag 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 number in only one circle on the diagram. 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