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Tenth Grade (Grade 10) Represent and Determine Probability Questions

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Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.2
The probability of flipping a head on a fair coin is 0.5. What is the probability that you will flip 12 heads in a row?
  1. 2.4×10-4
  2. 6.0
  3. 1.6×10-7
  4. 0.5×10-12
Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.3
Mary is doing an experiment where she chooses two marbles, one after the other without replacement, from a bag of marbles. The bag of consists of 5 green, 6 red, and 9 blue marbles. She wants to find the probability that she chooses a blue marble given that she chose a green marble first. She lets G be the event that she chooses a green marble and B be the event that she chooses a blue marble. Mary reasons that, since P(G)=14 and P(B)=920, P(G then B)=980. (She uses "then" instead of "and" because the events happen one after the other). Therefore, she determines that P(B∣G)=920. Is she correct, and why?
  1. Yes, her assumptions and steps are all correct.
  2. No, she assumed that G and B are independent when they are not. P(G then B)=976, and therefore P(B∣G)=919.
  3. No, she calculated P(G then B) incorrectly. P(G then B)=1420=710, and therefore P(B∣G)=145.
  4. No, she found P(G then B), when this is unnecessary. Since the events are independent, she can simply say P(G)=P(G∣B).
Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.4
95 people were asked what type of soft serve ice cream they were most likely to buy. Their choices were vanilla, chocolate, and swirl (a combination of vanilla and chocolate). The chart shows the results. Which of the following statements are correct? There may be more than one correct answer.

VanillaChocolateSwirlTotal
Male622937
Female10272158
Total16493095
  1. There is almost no difference in probability in choosing someone who likes vanilla, whether choosing from all people, only men, or only women.
  2. It is nearly equally likely that you will choose someone at random who likes swirl, whether choosing from all people, only men, or only women.
  3. It is more likely that you will choose a man from people who like swirl, than if you choose from people who like vanilla.
  4. Randomly choosing a woman from people who like vanilla is more likely than choosing a woman from people who like chocolate.
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
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
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