G.PR.10

Solve problems involving the probability of compound events to make informed decisions; interpret expected value and measures of variability to analyze probability distributions.

G.PR.10.1Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events. Apply the Addition Rule conceptually, P(A or B)= P(A) + P(B)-P(A and B), and interpret the answers in context.G.PR.10.2Apply and interpret the general Multiplication Rule conceptually to independent events of a sample space, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)] using contingency tables or tree diagrams.G.PR.10.3Use conditional probability to interpret risk in terms of decision-making and investigate questions such as those involving false positives or false negatives from screening tests.G.PR.10.4Define permutations and combinations and apply this understanding to compute probabilities of compound events and solve meaningful problems.G.PR.10.5Interpret the probability distribution for a given random variable and interpret the expected value.G.PR.10.6Develop a probability distribution for variables of interest using theoretical and empirical (observed) probabilities and calculate and interpret the expected value.G.PR.10.7Calculate the expected value of a random variable and interpret it as the mean of a given probability distribution.G.PR.10.8Compare the payoff values associated with the probability distribution for a random variable and make informed decisions based on expected value and measures of variability.
Example Problems
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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