Pinworm infestation, which is commonly found in children, can be treated with the drug pyrantel pamoate. According to the Merck Manual, the treatment is effective in 90% of cases. Suppose that three children with pinworm infestation are given pyrantel pamoate.

a. Considering a success in a given case to be "a cure," formulate the process of observing which children are cured and which children are not cured as a sequence of three Bernoulli trials.

b. Construct a table similar to Table 5.14 on page 240 for the three cases. Display the probabilities to three decimal places.

c. Draw a tree diagram for this problem similar to the one shown in Fig. 5.4 on page 240.

d. List the outcomes in which exactly two of the three children are cured.

e. Find the probability of each outcome in part (d). Why are those probabilities all the same?

f. Use parts (d) and (e) to determine the probability that exactly two of the three children will be cured.

g. Without using the binomial probability formula, obtain the probability distribution of the random variable X, the number of children out of three who are cured.