The Venn diagram shows the number of students in a chorus, band, and/or orchestra

Problem 1

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.

Problem 2

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.

Problem 3

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".

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step-by-step explanation: