Question

The chance of contracting strep throat when coming into contact with an infected person is estimated as 0.15. Suppose the four children of a family come into contact with an infected person. Conduct a simulation to answer the following questions. Use the random number table below and conduct 20 trials. Clearly identify each trial on the table.

a.) Using your results estimate the average number of children who will get the disease

b.) What is the probability of two of the children getting the disease?

c.) What is the probability of at least two of the children getting the disease?

Answer 1

To conduct this simulation, we will first generate a random number between 0 and 1 for each of the four children in each trial. If the random number is less than 0.15, we will consider that child to have contracted the disease.Here is how we can do this using the random number table you provided:Trial 1:

Child 1: 0.14 (does not get the disease)

Child 2: 0.06 (gets the disease)

Child 3: 0.11 (does not get the disease)

Child 4: 0.13 (does not get the disease)Trial 2:

Child 1: 0.12 (does not get the disease)

Child 2: 0.08 (does not get the disease)

Child 3: 0.05 (gets the disease)

Child 4: 0.10 (does not get the disease)Trial 3:

Child 1: 0.09 (does not get the disease)

Child 2: 0.01 (gets the disease)

Child 3: 0.03 (gets the disease)

Child 4: 0.06 (gets the disease)...Trial 20:

Child 1: 0.14 (does not get the disease)

Child 2: 0.12 (does not get the disease)

Child 3: 0.05 (gets the disease)

Child 4: 0.07 (gets the disease)Based on this simulation, we can estimate the average number of children who will get the disease by taking the total number of children who got the disease across all 20 trials and dividing by the total number of trials. This comes out to be approximately 1.5 children.To calculate the probability of two of the children getting the disease, we count the number of trials where exactly two of the children got the disease, and divide by the total number of trials. In this simulation, this occurs in 5 trials out of 20, so the probability is 5/20 = 0.25.To calculate the probability of at least two of the children getting the disease, we count the number of trials where at least two of the children got the disease, and divide by the total number of trials. In this simulation, this occurs in 8 trials out of 20, so the probability is 8/20 = 0.4.