SUPP 2.6. A randomized controlled trial was conducted for the treatment of sinusitis among children.

• 60% of patients were randomized to treatment.
• 40% of patients were randomized to placebo.
• Among patients on treatment, 30% developed nausea.
• Among patients on placebo, 10% developed nausea.

Constructing a tree diagram is strongly recommended.Start with P(Treatment) = 0.6 and P(Placebo) =0.4.

a)Find the probability that a person did not develop nausea, given that they were taking placebo.

b)Find the probability that a person in the study was on placebo and developed nausea.

c)Find the probability that a person in the study developed nausea.

d)Given that a person developed nausea, find the probability that a person was on treatment.Use the tree diagram and the definition of conditional probability.

P(Trt|Nausea)=

e)Write a Bayes' formula in the context of this problem P(Trt|Nausea)=.

Here's a start:P(Trt|Nausea)=