Understand the rule first
Probability is favourable outcomes divided by all equally likely outcomes. A probability lies between 0 and 1, and an event plus its complement totals 1.
Probability 11+ practice
Calculate probabilities from equally likely outcomes and their complements.
A bag has 4 red, 3 blue and 1 green counter. Find P(blue).
- There are 4 + 3 + 1 = 8 counters.
- Three favourable counters are blue.
- P(blue) = 3/8.
A common misconception
Using the number of unwanted outcomes as the denominator instead of the total number of outcomes.
Reusable method: Confirm that every possible outcome has been counted once.Question 1 of 8 MathscoreA bag contains 3 red, 5 blue and 2 green counters. What is P(blue)?
- A1/5
- B2/5
- C3/5
- D1/2
Need a hint?
Count all counters before forming the fraction.
Show worked answer
Answer D: 1/2
There are 10 counters and 5 are blue, so 5/10 = 1/2.
Quick method: Confirm that every possible outcome has been counted once.
Question 2 of 8 MathscoreA fair six-sided die is rolled. What is P(rolling more than 4)?
- A1/3
- B1/6
- C1/2
- D2/3
Need a hint?
The favourable results are 5 and 6.
Show worked answer
Answer A: 1/3
Two of six outcomes are favourable, so 2/6 = 1/3.
Quick method: Confirm that every possible outcome has been counted once.
Question 3 of 8 MathscoreA spinner has 8 equal sectors, 3 yellow and 5 purple. What is P(not yellow)?
- A3/8
- B5/8
- C5/3
- D3/5
Need a hint?
Not yellow means purple.
Show worked answer
Answer B: 5/8
Five of the eight equal sectors are not yellow, so the probability is 5/8.
Quick method: Confirm that every possible outcome has been counted once.
Question 4 of 8 Mathsexam-styleTwo fair coins are tossed. What is P(getting exactly one head)?
- A1/4
- B3/4
- C1/2
- D1
Need a hint?
List HH, HT, TH and TT.
Show worked answer
Answer C: 1/2
HT and TH are two favourable outcomes from four, so the probability is 1/2.
Quick method: Confirm that every possible outcome has been counted once.
Question 5 of 8 Mathsexam-styleOne whole number is chosen at random from 1 to 12. What is P(choosing a multiple of 3)?
- A1/4
- B1/2
- C2/3
- D1/3
Need a hint?
Count 3, 6, 9 and 12.
Show worked answer
Answer D: 1/3
Four of twelve numbers are multiples of 3, so 4/12 = 1/3.
Quick method: Confirm that every possible outcome has been counted once.
Question 6 of 8 Mathsexam-styleA bag has 2 red, 3 blue and 5 yellow counters. What is P(not yellow)?
- A1/5
- B3/10
- C3/5
- D1/2
Need a hint?
Not yellow includes red and blue.
Show worked answer
Answer D: 1/2
Five of ten counters are not yellow, so the probability is 1/2.
Quick method: Confirm that every possible outcome has been counted once.
Question 7 of 8 Mathsexam-styleA spinner has 10 equal sectors and 4 are green. What is P(green)?
- A2/5
- B1/4
- C3/5
- D4/5
Need a hint?
Simplify 4/10.
Show worked answer
Answer A: 2/5
Four favourable sectors out of ten gives 4/10 = 2/5.
Quick method: Confirm that every possible outcome has been counted once.
Question 8 of 8 Mathsexam-styleA fair coin and a fair die are used. What is P(head and an even number)?
- A1/6
- B1/4
- C1/3
- D1/2
Need a hint?
Multiply P(head) by P(even).
Show worked answer
Answer B: 1/4
P(head) = 1/2 and P(even) = 3/6 = 1/2; 1/2 × 1/2 = 1/4.
Quick method: Confirm that every possible outcome has been counted once.