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Medical risks Morris鈥檚 kidneys are failing, and he is awaiting a kidney transplant. His doctor gives him this information for patients in his condition: 90% survive the transplant and 10% die. The transplant succeeds in 60% of those who survive, and the other 40% must return to kidney dialysis. The proportions who survive five years are 70% for those with a new kidney and

50% for those who return to dialysis.

(a) Make a tree diagram to represent this setting.

(b) Find the probability that Morris will survive for five years. Show your work.

Short Answer

Expert verified

Part (b) P(Survive5years)=55.8%

Part (a) The tree diagram is

Step by step solution

01

Part (a) Step 1. Given Information

Ninety percent of those who receive a kidney transplant survive, but ten percent die. The transplant is successful in 60%of individuals who survive, while the remaining 40% must return to dialysis. Those who receive a new kidney have a 70% chance of surviving five years, whereas those who return to dialysis have a 50% chance.

02

Part (a) Step 2. Explanation

There are two choices, therefore at each knot, two branches are needed:

Theprobability=ThenumberoffavorableoutcomesThetotalnumberofpossibleoutcomes

03

Part (b) Step 1. Concept Used

Multiplication rule P(ABC)=P(A)P(B)P(C)

04

Part (b) Step 2. Calculation

Now, for each sort of medical risk, determine the likelihood of paying using a credit card. P(Survive5yearsSucceedsSurvive)=90%60%70%

=0.90.60.7=0.3780

P(Survive5yearsReturntodialysisSurvive)=90%40%50%

=0.90.40.5=0.1800

Fill in the blanks with the corresponding probabilities:

P(Survive5years)=0.3780+0.1800P(Survive5years)=0.558P(Survive5years)=55.8%

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