Question 185977: Rewa asked 150 randomly chosen students what programmes they had watched the previous night
on television. Shortland Street was watched by 90 students, 50 students had watched NZ Idol, and
30 had watched both.
What is the probability that a randomly chosen student had watched neither Shortland Street nor
NZ Idol the previous night?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Rewa asked 150 randomly chosen students what programmes they had watched the previous night on television.
Shortland Street was watched by 90 students, 50 students had watched NZ Idol, and 30 had watched both.
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What is the probability that a randomly chosen student had watched neither Shortland Street nor NZ Idol the previous night?
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Use a Venn diagram so you can see the answer:
Draw a rectangle; label it 150
Draw two intersecting circles inside the rectangle
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Put 30 in the intersection.
Label one of the circles SS with a 90 and NZ with a 50.
Put a 60 in the part of SS that is not in the intersection.
Put a 20 in the part of NZ that is not in the intersection.
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Your problem
60+30+20 = 110 in the circles
So, 40 must be outside the circles
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What is the probability that a randomly chosen student had watched neither Shortland Street nor NZ Idol the previous night?
Therefore P(watched neither) = 40/150
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Cheers,
Stan H.
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