There is a $ 70 \% $ chance that a person eats dinner, a $ 50 \% $ chance a person eats dessert and a $ 35 \% $ chance the person will eat dinner and dessert. Which of the following is true?

A. Eating dinner and eating dessert are dependent events because $ P $ (dinner) $ -P $ (dessert) $ =0.7-0.5=0.2 $ which is less than $ P( $ dinner and dessert $ )=0.35 $.
B. Eating dinner and eating dessert are independent events because $ P( $ dinner $ )-P $ (dessert) $ =0.7-0.5=0.2 $ which is less than $ P( $ dinner and dessert) $ =0.35 $.
C. Eating dinner and eating dessert are dependent events because $ P( $ dinner $ ) \cdot P $ (dessert) $ =0.7 \cdot 0.5=0.35 $ which is equal to $ P( $ dinner and dessert $ )=0.35 $.
D. Eating dinner and eating dessert are independent events because $ P( $ dinner $ ) \cdot P( $ dessert $ )=0.7 \cdot 0.5=0.35 $ which is equal to $ P( $ dinner and dessert $ )=0.35 $.

Question

There is a $ 70 \% $ chance that a person eats dinner, a $ 50 \% $ chance a person eats dessert and a $ 35 \% $ chance the person will eat dinner and dessert. Which of the following is true?

A. Eating dinner and eating dessert are dependent events because $ P $ (dinner) $ -P $ (dessert) $ =0.7-0.5=0.2 $ which is less than $ P( $ dinner and dessert $ )=0.35 $.
B. Eating dinner and eating dessert are independent events because $ P( $ dinner $ )-P $ (dessert) $ =0.7-0.5=0.2 $ which is less than $ P( $ dinner and dessert) $ =0.35 $.
C. Eating dinner and eating dessert are dependent events because $ P( $ dinner $ ) \cdot P $ (dessert) $ =0.7 \cdot 0.5=0.35 $ which is equal to $ P( $ dinner and dessert $ )=0.35 $.
D. Eating dinner and eating dessert are independent events because $ P( $ dinner $ ) \cdot P( $ dessert $ )=0.7 \cdot 0.5=0.35 $ which is equal to $ P( $ dinner and dessert $ )=0.35 $.

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