Question

Scarlett is practicing math fluency. She has 100 math operation flashcards with 42 addition problem cards, 56 subtraction cards, and 2 multiplication cards. Scarlett will time herself to see how fast she can solve the problems on seven cards. She chooses her seven cards and they are all addition cards. Is choosing all addition cards likely? Explain by running a simulation. (10 points)

Part A: State the problem or question and assumptions. (2 points)

Part B: Describe the process for one repetition, including possible outcomes, assigned representations, and measured variables. (3 points)

Part C: Use digits from a table of random digits or use your calculator to perform one repetition. Submit the list of random digits and indicate those that represent addition cards. (3 points)

Part D: Suppose there was one repetition when all seven cards were addition cards after 200 repetitions of the simulation. State your conclusions from these results. (2 points)

Answer 1

Part (A) problem and assumptions

7 cards are drawn from 100 cards such that each set of 7 cards has an equal chance of being selected.

The problem is to examine the chance that all chosen 7 cards are addition cards.

Part (B) One repetition

Let use the representation: numbers 1 to 42 represent addition cards, numbers 43 to 98 represent subtraction cards, and numbers 99 and 100 represent multiplication cards.

Randomly choose 7 numbers from 1 to 100 without replacement.

The following set of 7 numbers are selected using a table of random numbers.

65 60 44 97 30 3 83

Among these numbers, 3 and 30 represent addition cards.

44,60,65,83 and 97 are subtraction cards.

There are no multiplication cards.

The outcome is 2 addition cards, 5 subtraction cards and no multiplication cards.

Part (C)

From part (B), the random digits are

65 60 44 97 30 3 83

The fifth and sixth cards, that is, 30 and 3 represent addition cards.

Part (D)

If the event (all 7 cards are addition cards) happens once in 200 repetitions, the estimated likelihood of the event is 1/200 = 0.005.