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Tenth Grade (Grade 10) Statistics and Probability Concepts Questions

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Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.6
Mia goes to East York Collegiate Institute. She is given the following information:

There are 150 grade 12 students at East York Collegiate Institute.
70 of the grade 12 students drive a car at the school.
Half of all students with a grade average of 90 or higher have a car.

She is asked to find the probability of randomly choosing a grade 12 student with a car, given that the student has an average grade of 90 or higher. She reasons initially that, since there are 70 grade 12 students out of 150 who have a car, it would be 7/15. However, since it is a conditional probability, she needs to multiply by 1/2, since the probability that a student with a grade average of 90 or higher is 1/2. This results in a probability of 7/30. Is she correct or not, and why?
  1. Yes, and her reasoning is correct.
  2. No, she didn't need to multiply by 1/2 and the probability is 7/15. The probability that a student has a car can be assumed to be independent of their grade average, and so no multiplication is needed.
  3. No, there is insufficient information to find this probability.
  4. No, she needs to state that it can be assumed that half of grade 12 students have an average of 90 or higher. Therefore, half of 70 is 35, half of 150 is 75, and the probability is 7/15.
Grade 10 Combinations and Permutations CCSS: HSS-CP.B.9
What is the formula for finding the probability of event A or event B, but not both?
  1. P(A) + P(B)
  2. P(A) - P(A and B)
  3. P(B) - P(A and B)
  4. P(A) + P(B) - 2 * P(A and B)
Grade 10 Combinations and Permutations CCSS: HSS-CP.B.9
What is the formula for finding the probability of an event given that it is not the complement of another event?
  1. P(A)
  2. 1 - P(A)
  3. P(A | complement of B)
  4. P(complement of B | A)
Grade 10 Combinations and Permutations CCSS: HSS-CP.B.9
What is the sum of all possible probabilities in a sample space equal to?
  1. 0
  2. 1
  3. 100%
  4. 50%
Grade 10 Combinations and Permutations CCSS: HSS-CP.B.9
If two events are independent, what is the formula for their joint probability?
  1. P(A) * P(B)
  2. P(A and B)
  3. P(A) + P(B)
  4. P(A | B)
Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.7
Jason and Eva are watching their friends play poker. They can see Josh's cards. Josh currently has four cards in his hand, and is about to receive his fifth and final card. He has the ace of clubs, two of clubs, three of clubs, and four of clubs. Jason and Eva agree that the best options for his next card would be the five of clubs, or any card in the clubs suit. Jason says that the probability of getting the five of clubs or any remaining club card is the same as simply the probability of getting any remaining club card. Eva disagrees, saying that the probability of simply getting any remaining club card would be different than the probability of getting any remaining club card or the five of clubs. Who is correct and why?
  1. Eva is correct, because the probability of the two events must be added together, which will be higher than the probability of either event by itself since both of these events have a probability greater than zero.
  2. Eva is correct, since when using the addition rule of probability, one must always add the two probabilities (in this case choosing the five of clubs and then choosing any remaining club card), and then subtract the probability that both events occur.
  3. Jason is correct, because the probability of choosing the five of clubs AND any remaining club card is equal to the probability of choosing the five of clubs. Using the addition rule, these cancel out and one is left with the probability of choosing any remaining club card.
  4. Jason is correct, since the probability of choosing the five of clubs is so low, that it can be ignored.
Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.1
The probability of an event occurring is 615. What is the probability of the complement?
  1. 35
  2. 45
  3. 53
  4. 156
Grade 10 Combinations and Permutations CCSS: HSS-CP.B.9
What is the formula for finding the conditional probability of two events A and B?
  1. P(A and B)
  2. P(A) * P(B)
  3. P(A | B)
  4. P(B | A)
Grade 10 Represent and Determine Probability CCSS: HSS-CP.A.3
Aaron is given the following situation. There are 35 students in a class, 7 of which have a 90+ grade average. He chooses two students at random, one after the other. Let choosing a student with a 90+ grade average be event A, and choosing a student with an average below a 90 be event L. He wants to know whether these events are independent or dependent. Which is it, and why? Choose all correct answers.
  1. The events are dependent. After the first student has been chosen, there are fewer students, and so the probability of choosing the second student will be different than if the second student had been chosen from the full group of students.
  2. The events are dependent. Since P(L)=45, P(L∣A)=1417, and these are not equal, the events are dependent.
  3. The events are dependent. P(A then L)=385 and P(A)⋅P(L)=425. Since these are not equal, the events are not independent, and must be dependent.
  4. The events are independent. Because choosing the first student as a 90+ average student doesn't change the number of students with an average below 90, the probability will remain the same regardless of the first event.
Grade 10 Collecting and Interpreting Data CCSS: HSS-CP.A.1
Let A={numbers greater than 5} and B={numbers less than 12}. What is A∩B?
  1. {numbers between 5 and 12}
  2. {all numbers}
  3. {numbers less than 5 and greater than 12}
  4. {5,12}
Grade 10 Represent and Determine Probability CCSS: HSS-MD.A.1
What is the sample space of a fair 6 sided dice?
  1. {1, 2, 3, 4, 5, 6}
  2. {1, 6}
  3. {2, 4, 6}
  4. {1, 2, 3}
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