Question

Find the probability that a student is not playing a sport or not taking a foreign

language using the Venn Diagram below.

Answer 1

Answer: B) 18/25

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Step-by-step explanation:

The wording your teacher provided is a bit strange in my opinion. Though I think they are referring to the people who aren't taking both classes at the same time, but they could be taking exactly one class.

We have 23+14+10+3 = 50 students total and 14 of them are taking both classes. So 50-14 = 36 students are taking exactly one class, or they are taking neither of the classes.

This leads to a probability of 36/50 = (2*18)/(2*25) = 18/25 which points to choice B as the answer.

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Side note:

If it asked "what is the probability that a student is not taking a sport AND not taking a foreign language?", then the probability would be 3/50 because there are 3 people not taking either class out of the 50 total. So the keyword "and" is the change made here, instead of the "or".

Answer 2

18/25

Step-by-step explanation:

Total number of students = 23+14+10+3 = 50.

14 out of 50 are playing sport and taking a foreign language.

So the answer is (50 - 14) / 50

= 36/50

= 18/25.