Compute probability of an event from counts or a described sample space. | Probability and conditional probability | SAT Math

Probability is favorable outcomes divided by total outcomes.

Core Idea

Probability equals favorable outcomes divided by total outcomes. Identify both counts correctly and the arithmetic takes care of itself.

Understanding

The formula is simple:

𝑃 (e v e n t) = n u m b e r o f f a v o r a b l e o u t c o m e s t o t a l n u m b e r o f o u t c o m e s

The SAT tests whether you can identify those two numbers in context — from a word problem, a list, or a data set.

When a problem says "a marble is chosen at random from a bag containing 5 red, 3 blue, and 2 green marbles," the total is $5 + 3 + 2 = 10$ . The favorable count depends on what's asked: if it's red, the numerator is 5, so $𝑃 (r e d) = 510 = 12$ .

The most common error is using an incomplete total. Students sometimes forget one category or use only part of the data. Always add up every group to get the true denominator.

Probabilities are always between 0 and 1 (or 0% and 100%). If your answer falls outside that range, something went wrong with your counts.

Step by Step

Read the problem and list every category or outcome with its count.
Add all counts to find the total number of outcomes.
Identify which outcomes are 'favorable' — the ones the question asks about.
Divide: favorable / total. Simplify if needed.

Misconceptions

Using only some categories in the total instead of all categories.
Confusing 'at least one' with 'exactly one' — 'at least one red' includes getting two reds, three reds, etc.
Forgetting to account for items that belong to more than one group when categories overlap.

Question

Worked Example

A jar contains 12 strawberry candies, 8 lemon candies, and 5 mint candies. If one candy is selected at random, what is the probability that it is NOT a lemon candy?

Select an answer to see the explanation