1. Suppose that you have ten cards. Five are red, three are yellow and two are...

1. Suppose that you have ten cards. Five are red, three are yellow and two are blue. The five red cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The two blue cards are numbered 1 and 3. The cards are well shuffled. You randomly draw one card. Let R be the event that the card drawn is red and O be the event that the card drawn is odd-numbered. Find Pr(R|O).

2. Suppose you flip two fair coins simultaneously. Let A and B denote respectively the event of getting a head for the first coin and the event of getting a tail for the second coin. Which of the following statements do you think is incorrect?

	A.	The events A and B are mutually independent.
	B.	Pr(A) + Pr(B) = 1.
	C.	Pr(A or B) = 3/4.
	D.	The events A and B are mutually exclusive.

3. Suppose A and B are two mutually independent events such that Pr(A)=1 and Pr(B)=1. Which of the following statements is incorrect?

	I.	Pr(A\|B)=Pr(A).
	II.	Pr(A or B)=1.
	III.	Pr(A and B)=1.
	IV.	Pr(A or B) = Pr(A) + Pr(B).

4. Suppose A and B are two mutually exclusive events with Pr(A)=0.5 and Pr(B)=0.5. Which of the following statements do you think is correct?

	I.	Pr(A\|B)=Pr(A).
	II.	Pr(B\|A)=Pr(B).
	III.	Pr(A and B)=0.5.
	IV.	Pr(A or B) = 1.

5. Suppose J and K are two independent events such that Pr(J|K) = 0.37.

Find P(J'), where J' denotes the complement of event J.

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1. Suppose that you have ten cards. Five are red, three are yellow and two are...

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