Represent and Determine Probability Question
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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.
- 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.
- The events are dependent. Since P(L)=45, P(L∣A)=1417, and these are not equal, the events are dependent.
- 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.
- 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.