Construct a Venn diagram of the probabilities from the teacher's survey. Based on the probabilities, are the events "course grade was a C" and "did at least 30 minutes of homework" independent? Explain your answer.

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Step-by-step explanation:

A Venn diagram of these probabilities would look exactly like the body of the table. It would have 6 non-overlapping cells completely covering the universe. Pairs would be identified as associated with the same grade, and triples would be identified as associated with homework time.

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P(C | ≥30) = P(C and ≥30)/P(≥30)

P(C | ≥30) = 0.07/0.70 = 0.1

P(C) = 0.2 ≠ 0.1 = P(C | ≥30)

The events are not independent. The probability of a grade of C depends on how much homework was done.

the probability is 0