Probability of choosing from objects that are not distinct
Three categories, and the question asks about the one you do not want. Count everything else, or subtract. Subtracting is fewer steps and fewer chances to drop a number.
A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
A car lot has 4 sedans, 9 SUVs and 7 trucks. One is chosen at random.
What is the probability it is not an SUV? Write it as a fraction.
A crate holds 6 apples, 8 oranges and 11 pears. One is taken at random.
Probability it is not a pear? Write it as a fraction.
5 blue, 5 red and 10 green counters. A student answered 10/10 for the probability of drawing a counter that is not green.
What is the correct answer? Write it as a fraction.
A shelf holds 5 mysteries, 13 romances and 7 biographies. One book is chosen at random.
What is the probability that the book chosen is not a romance?
Write your answer as a fraction.
The total
Which way to count?
The favourable count
As a fraction
The complement is almost always shorter
12/25. Reached by subtracting one number rather than adding two.
With three categories the saving is small. ALEKS also asks this with four and five categories, and there the complement is the difference between one subtraction and four additions with a chance to drop one. Build the habit now, on the easy version.