Consider the following experiment. A playing card is drawn from a deck of 52 cards and replaced, then a second card is drawn. The associated sample space ? consists of pairs which record the suit and denomination of the two cards drawn. Let A be the event, "the first card is a spade. Let B be the event, "the second card is a spade." Let C be the event, "both cards have the same color." Please recall that playing cards are either red, the hearts and diamonds, or black, the spades and clubs. Determine whether a.) A and B are independent. b.) B and C are independent. c.) A, B, and C are independent.

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Chapter1: Combinatorial Analysis
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**Conditional Probability and Independence of Events**

Consider the following experiment. A playing card is drawn from a deck of 52 cards and replaced, then a second card is drawn. The associated sample space \( \Omega \) consists of pairs which record the suit and denomination of the two cards drawn. Let \( A \) be the event, "the first card is a spade." Let \( B \) be the event, "the second card is a spade." Let \( C \) be the event, "both cards have the same color." Please recall that playing cards are either red, the hearts and diamonds, or black, the spades and clubs.

Determine whether

a.) \( A \) and \( B \) are independent.

b.) \( B \) and \( C \) are independent.

c.) \( A \), \( B \), and \( C \) are independent.
Transcribed Image Text:**Conditional Probability and Independence of Events** Consider the following experiment. A playing card is drawn from a deck of 52 cards and replaced, then a second card is drawn. The associated sample space \( \Omega \) consists of pairs which record the suit and denomination of the two cards drawn. Let \( A \) be the event, "the first card is a spade." Let \( B \) be the event, "the second card is a spade." Let \( C \) be the event, "both cards have the same color." Please recall that playing cards are either red, the hearts and diamonds, or black, the spades and clubs. Determine whether a.) \( A \) and \( B \) are independent. b.) \( B \) and \( C \) are independent. c.) \( A \), \( B \), and \( C \) are independent.
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