Lessons · Quantitative Reasoning
CLT Quantitative Reasoning · Lesson
Counting and probability
Probability is favorable outcomes ÷ possible outcomes. For counting, multiply the choices at each step; for "and" multiply probabilities, for "or" (when they cannot both happen) add.
- List or count the total outcomes. Two dice have 6 × 6 = 36.
- Count the outcomes you want, carefully and without double counting.
- For arrangements, multiply: 4 books on a shelf can be arranged 4 × 3 × 2 × 1 = 24 ways.
Q. Two fair dice are rolled. What is the probability that the sum is 7?
Answer 1/6
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1): 6 of 36 outcomes.
- Counting (3,4) and (4,3) as one outcome. On two dice they are different.
- Adding probabilities for "and" events.
Every practice question comes with a full explanation, including why each wrong choice is wrong. Free, with no account.