Annotation
• In Part A, the student gives the correct probability of drawing a yellow card after two cards are drawn and then replaced.
• In Part B, the student explains how the probability with replacement was determined. The student found the total number of cards, and created a fraction in simplest form with the number of yellow cards in the numerator and the total number of cards in the denominator. The student correctly states that the probability of drawing a yellow card increases when the two previously drawn cards are not replaced. This conclusion is justified by comparing the values of the two probabilities.

Maria has a deck of cards with 10 red cards, 12 black cards, and 18 yellow cards.

Part A Maria draws a red card followed by a black card, and then replaces both of them. Next, Maria randomly draws another card. What is the probability that this card is yellow?

Part B Use what you know about probability to explain how you determined your answer. Use words and/or numbers to support your explanation. Maria draws a red card followed by a black card, and does not replace them. Use what you know about probability to justify why she is less likely or more likely to randomly draw a yellow card when she does not replace the red and black card. Use words and/or numbers to support your justification.

Student 2 Response

Annotation
• In Part A, the student gives the correct probability of drawing a yellow card after two cards are drawn and then replaced.
• In Part B, the student explains how the probability with replacement was determined. The student found the total number of cards, and created a fraction with the number of yellow cards in the numerator and the total number of cards in the denominator. The fraction was then written in decimal form. The student correctly states that the probability of drawing a yellow card is more likely when the two previously drawn cards are not replaced. This conclusion is justified by comparing the values of the two probabilities.

Maria has a deck of cards with 10 red cards, 12 black cards, and 18 yellow cards.

Part A Maria draws a red card followed by a black card, and then replaces both of them. Next, Maria randomly draws another card. What is the probability that this card is yellow?

Part B Use what you know about probability to explain how you determined your answer. Use words and/or numbers to support your explanation. Maria draws a red card followed by a black card, and does not replace them. Use what you know about probability to justify why she is less likely or more likely to randomly draw a yellow card when she does not replace the red and black card. Use words and/or numbers to support your justification.

Annotation
• In Part A, the student gives the correct probability of drawing a yellow card after two cards are drawn and then replaced.
• In Part B, the student explains how the probability with replacement was determined. The student found the total number of cards, and created a fraction with the number of yellow cards in the numerator and the total number of cards in the denominator. The student used a similar process to correctly determine the probability of drawing a yellow card after two cards are drawn without being replaced. The response does not state or justify why a yellow card is less likely or more likely to be randomly drawn when the two cards drawn earlier are not replaced.

Maria has a deck of cards with 10 red cards, 12 black cards, and 18 yellow cards.

Part A Maria draws a red card followed by a black card, and then replaces both of them. Next, Maria randomly draws another card. What is the probability that this card is yellow?

Part B Use what you know about probability to explain how you determined your answer. Use words and/or numbers to support your explanation. Maria draws a red card followed by a black card, and does not replace them. Use what you know about probability to justify why she is less likely or more likely to randomly draw a yellow card when she does not replace the red and black card. Use words and/or numbers to support your justification.

Student 4 Response

Annotation
• In Part A, the student gives the correct probability of drawing a yellow card after two cards are drawn and then replaced.
• In Part B, the explanation for determining the probability with replacement is missing. The student correctly states that a yellow card is more likely to be picked after the two previously drawn cards are not replaced. This conclusion is justified by comparing the values of the two probabilities.

Maria has a deck of cards with 10 red cards, 12 black cards, and 18 yellow cards.

Part A Maria draws a red card followed by a black card, and then replaces both of them. Next, Maria randomly draws another card. What is the probability that this card is yellow?

Part B Use what you know about probability to explain how you determined your answer. Use words and/or numbers to support your explanation. Maria draws a red card followed by a black card, and does not replace them. Use what you know about probability to justify why she is less likely or more likely to randomly draw a yellow card when she does not replace the red and black card. Use words and/or numbers to support your justification.

Annotation
• In Part A, the student gives the correct probability of drawing a yellow card after two cards are drawn and then replaced.
• In Part B, the student explains how the probability with replacement was determined. The student found the total number of cards, and created a fraction in simplest form with the number of yellow cards in the numerator and the total number of cards in the denominator. The student did not respond to the question about the probability of picking a yellow card after the two previously drawn cards are not replaced.

Maria has a deck of cards with 10 red cards, 12 black cards, and 18 yellow cards.

Part A Maria draws a red card followed by a black card, and then replaces both of them. Next, Maria randomly draws another card. What is the probability that this card is yellow?

Part B Use what you know about probability to explain how you determined your answer. Use words and/or numbers to support your explanation. Maria draws a red card followed by a black card, and does not replace them. Use what you know about probability to justify why she is less likely or more likely to randomly draw a yellow card when she does not replace the red and black card. Use words and/or numbers to support your justification.

Student 6 Response

Annotation
• In Part A, the student gives the correct probability of drawing a yellow card after two cards are drawn and then replaced.
• In Part B, the explanation for determining the probability with replacement is missing. The student determines the probability of drawing a yellow card after two cards are drawn without being replaced. The response does not state or justify whether randomly picking a yellow card is less likely or more likely to occur when the two previously drawn cards are not replaced.

Maria has a deck of cards with 10 red cards, 12 black cards, and 18 yellow cards.

Part A Maria draws a red card followed by a black card, and then replaces both of them. Next, Maria randomly draws another card. What is the probability that this card is yellow?

Part B Use what you know about probability to explain how you determined your answer. Use words and/or numbers to support your explanation. Maria draws a red card followed by a black card, and does not replace them. Use what you know about probability to justify why she is less likely or more likely to randomly draw a yellow card when she does not replace the red and black card. Use words and/or numbers to support your justification.