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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?

[math] "Janet" [/math][math] "Cam"[/math][math] "Mike" [/math]
[math] 4 [/math][math] 0 [/math][math] 0 [/math]
[math]3[/math][math] 1[/math][math]0 [/math]
[math]3[/math][math]0 [/math][math]1[/math]
[math]2[/math][math]2 [/math][math]0[/math]
[math]2[/math][math]0 [/math][math]2[/math]
[math]2[/math][math]1 [/math][math]1[/math]
[math]1[/math][math]3 [/math][math]0[/math]
[math]1[/math][math]0 [/math][math]3[/math]
[math]1[/math][math]2 [/math][math]1[/math]
[math]1[/math][math]1 [/math][math]2[/math]
[math]0[/math][math]4 [/math][math]0[/math]
[math]0[/math][math]0 [/math][math]4[/math]
[math]0[/math][math]3 [/math][math]1[/math]
[math]0[/math][math]1 [/math][math]3[/math]
[math]0[/math][math]2 [/math][math]2[/math]
  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

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