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Common Core Standard HSS-CP.B.6 Questions

Find 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.

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Grade 10 Represent and Determine Probability CCSS: HSS-CP.B.6
Janet, Cam, and Mike arrive at a school party and there are only four cupcakes left. Everyone else has eaten enough cupcakes and will eat no more. Below is table of all possible ways these four cupcakes could be eaten by these three people. How likely it is that Janet will eat more cupcakes than Cam and Mike, given that before Janet gets to the cupcake table, Cam and Mike have already each eaten a cupcake?

JanetCamMike
400
310
301
220
202
211
130
103
121
112
040
004
031
013
022
  1. 4/15, because there are only four possible scenarios in which Janet eats more cupcakes out of the total 15 possibilities.
  2. 3/14, since for row 1, neither Cam nor Mike has had a cupcake.
  3. 1/12, because rows 1-3 don't count, as they have Mike and Cam eating only one cupcake between them (and two need to have been already eaten).
  4. 1/6, since rows 1-5, 7, 8, 11, 12 aren't included as they don't have Cam and Mike as having eaten at least one cupcake each.
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.

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