Pinworm infestation, commonly found in chidren, can be treated with the drug tha

Question

Pinworm infestation, commonly found in chidren, can be treated with the drug that is effective in 81% of cases. Suppose that three children with pinworm infestation are given the drug "4 a. Construct a table that gives the probability for each outcome. (Let s be a success and fbe a failure.) Probability s5S ssf sfs sff fss fsf fs (Round to three decimal places as needed.) b. Draw a tree diagram for this problem Choose the correct tree diagram below. A. ??. ??. esfs fsf ffs c. List the outcomes in which exactly two of the three children are cured. (Let s be a success and f be a failure.) (Use a comma to separate answers as needed.) d. Find the probability of each outcome in part (c). Why are those probabilities all the same? Each outcome in part (c) has the probability Round to three decimal places as needed.) Why are those probabilities all the same? O A. The probability is the same for each outcome because each probability is obtained by multiplying two success probabilities of 0.81 and one failure probability of 0.19 O B. The probability is the same for each outcome because each probability is obtained by multiplying one O C. The probability is the same because each outcome is the same. e. Use parts (c) and (d) to determine the probability that exactly two of the three children will be cured success probability of 0.19 and two failure probabilities of 0.81. P(exactly two children are cured)- (Round to three decimal places as needed.) f. 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 P(X x) (Round to three decimal places as needed.)

Explanation / Answer

Ans a The probability of s is .81

So the probability of ss that is probability of success in both 1st and 2nd children is 0.81 * 0.81 since it is independent for them thus the required probabilities is

sss = 0.813 = 0.5314

ssf = 0.81 * 0.81 * 0.19 = .1246

sfs = 0.81 * 0.19 * .81 = .1246

sff = 0.81 * 0.19 * 0.19 = 0.0292

fss = 0.19 * 0.81 * 0.81 = 0.1246

fsf = 0.19 * 0.81 * 0.19 = 0.0292

ffs = 0.19 * 0.19 * 0.81 = 0.0292

fff = 0.193 = 0.00685

Ans b Is option c basically for the first children it can s or f .For it being s for the 1st childran it can s or f for the 2nd childran and same for f being for 1st child.And this follows for third child.

Ans c The possible outcomes for which 2 children are cured is ssf , sfs and fss

Ans d For all of the 3 possible outcomes the probability is 0.812 * 0.19 = 0.1246 = 0.125

(A) It is same for all the three outcomes because for all the three children the probability of s=0.81 is same and the outcome for 1 child is independent from other.

Ans e P( exactly 2 children are cured) = 3 * 0.125 = 0.375

Ans f P(X= 0) = fff = 0.00685

         P(X = 1 ) = ffs,sff,fsf = 3 * 0.0292 = 0.0876

         P(X = 2 ) = 0.375

         P(X=3) = 0.5314

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