Problem 1
Answer: 1/6
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Work Shown:
5 people play tennis or soccer
6+5+9+10 = 11+19 = 30 people total
5/30 = (1*5)/(6*5) = 1/6 is the probability of picking someone who plays tennis or soccer.
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Problem 2
Answer: 1/5
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Work Shown:
6 people play tennis, but not soccer.
There are 30 people total (calculated earlier in problem 1).
6/30 = (1*6)/5*6) = 1/5 is the answer
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Problem 3
Answer: 5/11
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Work Shown:
5+6 = 11 people play tennis
We focus on these people only due to the phrasing "given they play tennis"
Earlier in the problem, we're asked the probability of someone playing soccer but not tennis; however, this contradicts the "given they play tennis" fact.
Since the two clash, it means that the probability is 0. There is no way that someone plays tennis and not plays tennis at the same time.
If your teacher means to ask "what is the probability of a student playing soccer given they play tennis also?", then the answer would be 5/11 since we have 5 students who play both and 11 students who play tennis.
I have a feeling your teacher meant to ask this, but I'm not 100% sure. I would double check with your teacher.
