Are drawing a black and red card independent or mutually exclusive?

Are drawing a black card and queen independent?
Are drawing a face card and queen independent?

2 answers

A black and red card are independent because you cannot draw a black card that is also a red card.

A black card and a queen are not independent because you can draw a card that is both black and a queen.

A face card and a queen are not independent because you can draw a card that is both a face card and a queen.
You are buying orange juice for $4.50 per container and have a gift card worth $7.00. The function f(x) = 4.50x - 7represents your total cost f(x) if you buy x containers of orange juice and use the gift card. How much do you pay to buy 4 containers of orange juice? How about if you buy 6?
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