Basic Probability
Probability of a single event is a ratio: favorable outcomes over total outcomes.
Reading the concept isn't enough. The score comes from practicing the real Bluebook-style format and finding the exact mistakes you keep making.
What the SAT tests here
$P(\text{event}) = \frac{\text{favorable}}{\text{total}}$. Count the total outcomes correctly — especially when not all outcomes are equally likely.
How to solve one, step by step
Example: a bag has $3$ red and $5$ blue marbles. $P(\text{red})$?
- Favorable: $3$ red. Total: $3 + 5 = 8$.
- $P(\text{red}) = \frac{3}{8}$.
The mistakes that cost points
- Reporting a count, not a ratio. Probability is favorable over total, not just the favorable count.
- Miscounting total outcomes. Include every possible outcome in the denominator.
Practice questions
Try these the way you would on test day, then open the solution to check your method.
Easy
The table shows the number of students in each grade who participated in a school science fair. What fraction of all participants were 10th graders?
- A$\frac{4}{10}$
- B$\frac{24}{30}$
- C$\frac{4}{15}$
- D$\frac{30}{90}$
Show solution
Answer: C, $\frac{4}{15}$. Total $= 18 + 24 + 30 + 18 = 90$. 10th graders $= 24$. Fraction $= \frac{24}{90} = \frac{4}{15}$.
Medium
The table shows the number of defective and non-defective items produced by two machines. If one item is selected at random from Machine B's output, what is the probability it is defective?
- A$\frac{188}{200}$
- B$\frac{12}{200}$
- C$\frac{12}{400}$
- D$\frac{20}{400}$
Show solution
Answer: B, $\frac{12}{200}$. Machine B defective $= 12$. Machine B total $= 200$. $P = \frac{12}{200} = \frac{3}{50}$.
Hard
A weighted die is known to land on 6 twice as often as any other number. If the probabilities of rolling 1 through 5 are each $p$, and the probability of rolling 6 is $2p$, what is the probability of rolling a 6?
- A$2$
- B$\frac{1}{6}$
- C$\frac{5}{7}$
- D$\frac{2}{7}$
Show solution
Answer: D, $\frac{2}{7}$. The probabilities must sum to 1: $5p + 2p = 7p = 1 \Rightarrow p = \frac{1}{7}$. $P(6) = 2p = \frac{2}{7}$.
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