Probability — Digital SAT Math practice
Simple, compound and geometric probability.
Key terms
- Sample Space: The complete set of all possible outcomes for a given experiment or scenario.
- Independent Events: Two events where the outcome of one does not change the probability of the other.
- Dependent Events: Two events where the outcome of the first event changes the probability of the second.
- Complement: The set of all outcomes in the sample space that are not part of a given event.
- Favorable Outcomes: The specific results that satisfy the condition stated in the problem.
- Total Outcomes: The complete number of possible results available for the experiment.
Common traps
- Adding probabilities instead of multiplying them when finding the chance of two independent events happening together.
- Forgetting to reduce the denominator after removing an item in dependent probability problems.
- Using the total group size as the denominator when the question specifies a restricted subgroup.
Key ideas to know
Basic Probability Range & Formula
What is the probability of drawing a red marble from a bag with 3 red and 7 blue marbles? Also, what values can any valid probability take?
3/10 or 0.3. All probabilities must be between 0 and 1 inclusive.
Watch out: Forgetting to simplify fractions or writing decimals outside the 0-1 range.
Independent Events Multiplication Rule
If P(raining) = 0.4 and P(windy) = 0.5, and the events are independent, what is P(raining and windy)?
Multiply them: 0.4 × 0.5 = 0.2. Independent events always use multiplication for 'and'.
Watch out: Adding the probabilities instead of multiplying, which would give 0.9 (over 1).
Identifying the Correct Total for Probability
A class has 10 boys and 15 girls. If a student is chosen at random, what is the total number of outcomes to use in the denominator?
Use the whole group: 10 + 15 = 25 students. Only switch to a subgroup if the question specifies a restricted pool.
Watch out: Using only the subgroup count as the denominator instead of the full group total.
The Complement Rule Error
A student finds P(not winning) by calculating 10 − 0.2 = 9.8 because there are 10 total tickets. What is the correct method and answer if P(win) = 0.2?
Subtract from 1, not from ticket count: 1 − 0.2 = 0.8. The complement rule always uses 1 as the base for probabilities.
Watch out: Subtracting the probability from the number of possible outcomes instead of using 1.
Sample questions
Question 1
A bag contains 3 red, 3 blue, and 7 green marbles. If one marble is selected at random, what is the probability that it is red?
- 1/3
- 10/13
- 3/10
- 3/13
Show answer and explanation
Answer: 3/13
P(red) = 3/13.
Question 2
A bag contains 3 red, 5 blue, and 2 green marbles. If one marble is drawn at random, what is the probability that it is NOT blue?
- 1/2
- 5/10
- 3/10
- 2/5
Show answer and explanation
Answer: 1/2
Not blue = 3 + 2 = 5 of 10 marbles, so the probability is 5/10 = 1/2.