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Common Core Standard HSS-CP.B.8 Questions

(+) 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.

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Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.8
Given that P(A) = 0.71, P(B) = 0.22, and P(A|B) = 0.13, what is P(A and B)?
  1. 0.03
  2. 0.04
  3. 0.09
  4. 0.42
Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.8
Given a 12-sided die, with the numbers 1 through 12 on the sides, what is the probability that a prime number is rolled, given that the roll is a factor of 60? Choose the answer that correctly represents this.
  1. 1438
  2. 14512
  3. 35⋅51223
  4. 38⋅23512
Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.8
There are 26 students in Mr. Hinthorne's class. There are 12 male students. Of the male students, 3 wear glasses. 6 of the female students wear glasses. Let G represent choosing a person with glasses and F a female student. Which of the following are correct applications of the Multiplication Rule? Choose all that apply.
  1. P(F)=926⋅3723
  2. P(F∣G)=713⋅37926
  3. P(FandG)=713⋅926
  4. P(G∣F)=313713
Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.8
Given that P(A and B) = 0.14, P(A) = 0.55, and P(B) > P(B|A), what is P(A|B)?
  1. 0.25
  2. 0.08
  3. 0.55
  4. Not enough information.
Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.8
At Monarch Collegiate Institute, a survey was conducted about the number of students who play rugby and the number of students who read science fiction books. Let R be the event that a student plays rugby, and S be the event that a student reads science fiction books. If there were 60 students surveyed, P(R|S) = 5/7, P(S|R) = 1/3, and P(S) = 7/60, which of the following expressions gives the number of students who said they play rugby and why? Choose all correct answers.
  1. 60(760⋅5713), by applying the general Multiplication Rule to find P(R), then multiplying by 60.
  2. 60(1-760+(760⋅57)), since it can assumed that everyone who doesn't read science fiction plays rugby. Therefore, subtract P(S) from one, but add back in P(S and R) (found using the general Multiplication Rule), and then multiply by 60.
  3. 760⋅13=7180=P(S and R),   60(718057), by applying the general Multiplication Rule to find P(S and R), then using it again to find P(R) and then multiplying by 60.
  4. Not possible. If 60 is multiplied by 5/7 (the conditional probability of choosing someone who plays rugby, given that they read science fiction), the number is not a whole number. This means that either the total number of participants or this probability is incorrect.
Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.8
Given that P(A) = 0.31, P(A|B) = 0.48, and P(B|A) = 0.15, what is P(B)?
  1. 0.48
  2. 0.23
  3. 0.99
  4. 0.10
Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.8
Given that P(A) = 0.61, P(B) = 0.33, and P(A|B) = 0.09, what is P(B|A)?
  1. 0.17
  2. 0.05
  3. 0.27
  4. 0.20

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