Question

Malachi is practicing math fluency. He has 100 math operation flashcards with 42 addition problem cards, 56 subtraction cards, and 2 multiplication cards. He will time himself to see how fast he can solve the problems on two cards. He chooses his two cards and they are both multiplication cards. Is choosing two multiplication cards likely? Explain by running a simulation.

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 multiplication cards. (3 points)

Part D: Suppose there were 5 times when both cards selected were multiplication cards after 1,500 repetitions of the simulation. State your conclusions from these results. (2 points)

Essay Submission

Answer 1

Malachi's likelihood of choosing two multiplication cards from a deck of 100 mixed operation cards is very low. A simulation with 1,500 trials showed only 5 instances of this happening, signaling it is an unlikely event.

Step-by-step explanation:

Part A: Problem Statement and Assumptions

The problem is to determine the likelihood of Malachi selecting two multiplication flashcards from a stack of 100 cards where there are 42 addition, 56 subtraction, and only 2 multiplication cards. The assumption is that each card has an equal chance of being selected.

Part B: Simulation Process

For one repetition, we represent the flashcards by numbers 1 to 100. The two multiplication cards are represented by two specific numbers - say 1 and 2. We use a random number generator to draw two numbers from this set to simulate the selection of two flashcards. The measured variable is whether both drawn cards are multiplication cards.

Part C: Running One Repetition

Using a calculator, we generate two random numbers between 1 to 100. Suppose the numbers generated are 53 and 78, which do not represent the multiplication cards. Thus, for this repetition, Malachi did not draw two multiplication cards.

Part D: Conclusion from Simulation Results

After 1,500 repetitions, if there were only 5 instances where both cards were multiplication cards, it suggests that drawing two multiplication cards is quite unlikely, as this occurred in only a small fraction of the trials.

Answer 2

Answer: It is highly unlikely to get both multiplication cards on the first try.

Part A The question asked is: there are two multiplication cards out of one hundred cards including forty-two addition problem cards and fifty-six subtraction cards.What are the odds of getting just the multiplication cards.The assumption is this we are talking about the first try.

Part B You make the multiplication cards, card#1 and card#2. All other cards are #3-100. Then you use the random number generator to see odds of two numbers out of one hundred, which is 0.02%. as I did 2/100 x 1/99 then multiply by 100 so.02

Part C I got 83 and 27as my first two numbers with my random number generator, So Malachi didn't get a multiplication card in this random test. card #1 and card #2 are the multiplication cards

Part D The percentage of the time that you'd expect both multiplication cards to be picked is 0.002 or .2%. The proportion of the time that it happened here is 5/1500=.00333 or .33%, which means that this is pretty much in line with what you'd expect

Step-by-step explanation: I got a 10/10 on 3.07 essay test for honors statistics.