<h3>
Answer: 5/6</h3>
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Work Shown:
- A = number who passed test, and did the hw
- B = number who passed test, but didn't do the hw
- C = number who failed test, but did the hw
- D = number who failed test, and didn't do the hw
With a class total of 19, we know that A+B+C+D = 19.
12 students passed the test, which leaves 19-12 = 7 people who failed the test.
Of these 7 people who failed the test, 4 of them didn't do the hw. This leads to D = 4.
Note how C+D = 7 becomes C+4 = 7 and it solves to C = 3.
Since 13 people did the hw, we can say A+C = 13. Plug in that value of C we found earlier, to find that A = 10.
Lastly, solving A+B = 12 leads to B = 2.
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To summarize what we found so far:
Now onto the question your teacher is asking: "What is the probability that a student completed the homework given that they passed the test?"
The key phrase here is "given that they passed the test". Because of this phrase, we'll ignore anyone who didn't pass. We'll focus solely on the 12 students who passed. Of those 12 who passed, we found that A = 10 people did the hw.
Therefore, the probability of picking someone who did the hw, given the passed the test, is 10/12 = 5/6
