S-CP: Conditional Probability and the Rules of Probability

Conditional Probability and the Rules of Probability

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Conditional Probability and the Rules of Probability formalizes sample spaces, events, and probability calculations. Set notation describes unions, intersections, and complements, and conditional probability is defined and calculated using two-way tables and tree diagrams. The multiplication and addition rules, along with independence, are applied to compound events and real-world scenarios.

S-CP.1Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).S-CP.2Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.S-CP.3Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.S-CP.4Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in 10th grade. Do the same for other subjects and compare the results.S-CP.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.S-CP.6Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.S-CP.7Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.S-CP.8(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.S-CP.9(+) Use permutations and combinations to compute probabilities of compound events and solve problems.
Example Problems
Let and .
What is ?
Two fair 6-sided dice are rolled. What is the probability that both show a prime number?
Write your answer as a fraction.
A bag contains 9 blue candies, 7 red candies and 5 green candies.
A candy is chosen from the bag at random.

Find the probability that the candy is: Not Orange
A letter is selected at random from the word F I B O N A C C I.

Find the probability that the letter is: Not A
Write your answer as a fraction or as a decimal rounded to the nearest hundredth.
A bag contains 9 blue candies, 7 red candies and 5 green candies.
A candy is chosen from the bag at random.

Find the probability that the candy is: Yellow
Goblins

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