Question

Rima is practicing math fluency. She has 100 math operation flashcards with 42 addition problem cards, 56 subtraction cards, and 2 multiplication cards. She will time herself to see how fast she can solve the problems on ten cards. She chooses her ten cards and they are all subtraction cards. Is choosing all subtraction 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 subtraction cards. (3 points)

Part D: Suppose there were 17 times when all ten cards were subtraction cards after 2,000 repetitions of the simulation. State your conclusions from these results. (2 points)

Answer 1

ANSWER:

Part A)

Yes X is a binomial random variable

As, there is a probability of success which is 1 in 8

and probability of failure which is 7 in 8

And number of trials = 9

Part B)

Mean is = n*p

N = 9

P = 1/8 = 0.125

N*p = 1.125

Standard deviation is given by √{n*p*(1-p)} = 0.99215674164

Part C)

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.125

N = number of trials = 9

R = desired success = >=3

P(x>=3) = p(3)+p(4)+p(5).....+p(9)

And as we know that sum of all the probabilities is equal to 1

So, p(x>=3) = 1 - p(x<3)

P(x>=3) = 1 - (p(0)+p(1)+p(2)

After substitution

P(x>=3) = 0.09189072251

We call an event unusual when the probability is less than 0.05

But here it is greater than 0.05