Set: HW 5 Ch 13 Username: MinhTrang.Pham001@umb.edu

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This HW set is due on November 1, 2024, 11:59:00 PM EDT.

Correct answers become available on November 1, 2024, 11:59:00 PM EDT.

Problem 1

A deck of cards is shuffled and the top two cards are placed face down on a table. True or false:

1. There is 1 chance in 4 for the first card to be a heart. Answer: [?/TRUE/FALSE]
2. There is 1 chance in 4 for the second card to be a spade. Answer: [?/TRUE/FALSE]
3. The chance of getting a heart and then a spade is: % [Enter answer in percent rounded to the nearest whole percent, like 12 for 0.1178 (=11.78%); do not enter the % sign.]

Problem 2

A standard deck of cards contains 52 cards: 4 aces, 12 face cards, and 36 numbered cards.

Enter answers below in percent rounded to the nearest whole percent, like 12 for 0.1178 (=11.78%); do not enter the % sign.

Two draws are made at random with replacement from such a deck.

1. What is the chance of getting a numbered card on the first draw? Answer: %
2. What is the chance of getting a numbered card on the second draw? Answer: %
3. What is the chance of getting a numbered card on the first draw and a numbered card on the second draw? Answer: %
4. What is the chance of not getting a face card in the two draws? Answer: %
5. What is the chance of getting a face card at least once in the two draws? Answer: %

Problem 3

Two draws are made at random from the box

. Enter answers below in percent rounded

to the nearest whole percent, like 12 for 0.1178 (=11.78%); do not enter the % sign.

Find the chance that 2 is drawn at least once—

1. if the draws are made with replacement. Answer: %
2. if the draws are made without replacement. Answer: %

Problem 4

Three cards are drawn from a well-shuffled deck and placed down on the table. Enter answers below in percent rounded to the nearest whole percent, like 12% for 0.1178 (=11.78%).

1. Find the chance that all of the cards are even-numbered. Answer: %
2. Find the chance that none of the cards are even-numbered. Answer: %
3. Find the chance that the cards are not all even-numbered. Answer: %

Problem 5

Two tickets are drawn at random without replacement from the box

. Enter answers

below in percent rounded to the nearest whole percent, like 12 for 0.1178 (=11.78%); do not enter the % sign.

1. Find the chance that the second ticket is 4. Answer: %
2. Find the chance that the second ticket is 4, given the first is 2. Answer: %
3. Find the chance that the second ticket is 4, given the first is 4. Answer: % Now find the same three chances, if the draws are made with replacement.
4. Find the chance that the second ticket is 4. Answer: %
5. Find the chance that the second ticket is 4, given the first is 2. Answer: %
6. Find the chance that the second ticket is 4, given the first is 4. Answer: %

Problem 6

A deck of cards is shuffled and two cards are drawn.

Enter answers below in percent rounded to the nearest whole percent, like 12 for 0.1178 (=11.78%); do not enter the % sign.

1. Find the chance that the second card is a club, given that first card is a club. Answer: %.
2. Find the chance that the first card is a club and the second card is a club. Answer: %

Problem 7

[In the questions below enter answers in percent rounded to the nearest 0.1 percent, like 11.8 for 0.1178 (=11.78%); do not enter the % sign.]

A die is rolled three times. What is the chance that—

1. all the rolls show 2 or more spots? Answer: %
2. none of the rolls show 2 or more spots? Answer: %
3. all the rolls show 1 spot? Answer: %
4. none of the rolls show 1 spot? Answer: %
5. not all the rolls show 2 or more spots? Answer: %
6. not all the rolls show 1 spot? Answer: %
7. at least one roll shows 1 spot? Answer: %
8. at least one roll shows 2 or more spots? Answer: %

Which two of the above 8 outcomes have the highest probability?

• A. a
• B. b
• C. c
• D. d
• E. e
• F. f
• G. g
• H. h

Problem 8

Find the chance that the highest number rolled is a four when a single die is rolled 7 times.

Answer: % [Answer in percent rounded to the nearest 0.1 percent, like 11.8 for 0.1178 (=11.78%); do not enter the % sign.]

1	2	2	1
1	2	3	4

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