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You take a standard deck of playing cards, and remove one card at random. You then draw a single card. Write S for the event

You take a standard deck of playing cards, and remove one card at random. You then draw a single card. Write S for the event that the card you remove is a six. Write N for the event that the card you remove is not a six. Write R for the event that the card you remove is red. Write B for the event the card you remove is black.

(a) Write A for the event you draw a 6. What is P(A given S) ?

(b) Write A for the event you draw a 6. What is P(A given N)?

(c) Write A for the event you draw a 6. What is P(A)?

(d) Write D for the event you draw a red six. Are D and A independent? why?

(e) Write D for the event you draw a red six. What is P(D)?

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