Probability Flip Practice Test Worksheets
Probability flip questions ask for the chance that something is not a particular colour or type. The key is to count the whole set, subtract the target group, and write the remaining chance as a fraction.
For students who know probability basics, but get stuck using complements and “not” outcomes quickly.
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What Do Probability Flip Questions Look Like?
Probability flip questions focus on complementary events—finding the chance that an event does not happen. Often called "1 minus" problems, they test whether you can spot when working backwards is faster than direct counting. Here is a worked example.
Count What Is Not Gold
Question: A bag contains 7 silver cubes, 8 gold cubes and 10 bronze cubes. One cube is picked at random. What is the probability that the cube is NOT gold?
Probability = 1725
Worked Method
Step 1: Total cubes = 7 + 8 + 10 = 25.
Step 2: Gold cubes = 8.
Step 3: NOT gold = 25 - 8 = 17.
Step 4: Probability = qualifying items ÷ total items = 1725. This is already in simplest form.
Tip: Keep all items in the denominator. Excluding a colour from the wanted outcome does not remove those items from the bag.
Rules to Help You Solve Probability Flip Questions
To solve probability flip questions like the example above, use the complementary rule to save calculation time. Follow these four rules:
🧮 Rule 1: Count the total first
Add every group in the bag before thinking about the named colour.
Example: 7 silver + 8 gold + 10 bronze = 25 cubes.
🎯 Rule 2: Identify the excluded colour
The colour after NOT is the excluded colour. Count items of every other colour as qualifying outcomes.
Example: For "NOT gold", gold is the excluded colour; silver and bronze qualify.
↩️ Rule 3: Flip with subtraction
Subtract the number of items of the excluded colour from the total to find how many items qualify.
Example: 25 total - 8 gold = 17 not gold.
½ Rule 4: Simplify the fraction
The probability is the qualifying count divided by the total count. Simplify by dividing the numerator and denominator by the same common factor.
Example: 2028 simplifies to 57.
Two More Worked Examples
Here are two more examples demonstrating fraction simplification and alternative counting methods.
Simplify the Answer
Question: Jenny has 12 silver gems, 8 gold gems and 8 bronze gems in a bag. One gem is drawn at random. What is the probability that the gem is NOT bronze?
Probability = 2028 = 57
Worked Method
Step 1: Total gems = 12 + 8 + 8 = 28.
Step 2: Bronze gems = 8.
Step 3: NOT bronze = 28 - 8 = 20.
Step 4: Probability = qualifying items ÷ total items = 2028. Divide both numbers by 4: 20 ÷ 428 ÷ 4 = 57.
Tip: Simplifying changes how the probability is written, not the chance of the event happening.
Check Your Answer with Another Method
Question: There are 4 pink counters, 4 black counters and 12 white counters in a bag. One counter is drawn at random. Find the probability that it is NOT black.
Probability = 1620 = 45
Worked Method
Step 1: Total counters = 4 + 4 + 12 = 20.
Step 2: Black counters = 4.
Step 3: NOT black = 20 - 4 = 16.
Step 4: Probability = qualifying items ÷ total items = 1620. Divide both numbers by 4 to get 45.
Check with another method: Add the colours that qualify: 4 pink + 12 white = 16. This agrees with 20 − 4 = 16, so the probability is again 45.
Tip: You can count the qualifying items directly or subtract the excluded items from the total. Both methods should give the same count.
