Problem 1
Answer: 9/50
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Work Shown:
Add up the items that are in "chorus" and "band" circles. So we have 4+5 = 9 people who are in both activities.
This is out of 10+4+7+5+16+8 = 50 students total.
So 9/50 is the probability of picking someone from chorus and band.
This choice isn't listed so I think your teacher made a typo. Double check to make sure you copied the problem exactly as your teacher gave it.
Side note: Choice A might have been intended to be 9/50 instead of 9/70.
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Problem 2
Answer: 14/50
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Work Shown:
There are 10+4 = 14 people in chorus but not in orchestra.
This is out of 50 total, so 14/50 is the answer.
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Problem 3
Answer: 13/36
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Work Shown:
There are 7+5+16+8 = 12+24 = 36 people in orchestra.
There are 5+8 = 13 people in band and orchestra.
13/36 represents the probability of picking someone from band given they are also in orchestra. Note how we focus on the orchestra circle only , and ignore every other circle. This is because we know the person is from orchestra due to the "given".
