Suppose you have a treatment for a rare disease. If you apply this treatment to

Question

Suppose you have a treatment for a rare disease. If you apply this treatment to a person, they have a 30% chance of recovery. Suppose you apply your treatment to six patients. Show all work using the formula, do not use software.

(a) (1 point) To ensure that this is a binomial random variable we must assume something about our trials/ patients. What do we have to assume about our trials (patients) that I did not explicitly state? Find n and p .

(b) (2 points) Find the probability that exactly three individuals recover.

(c) (3 points) Find the probability that 5 or 6 patients recover. (d) (2 points) Find the probability that at least one patient recovers. (Hint: use the complement rule.)

Explanation / Answer

a. p=0.3 and n=6. The assumptions are: The number of trials is fixed and There are two and only two outcomes, labelled as "success" and "failure"

b. P(3)=6C3*(0.3)3(0.7)3= 0.18522

c. P(5)+P(6)=6C5*(0.3)5(0.7) +(0.3)6 =0.010206+0.000729=0.010935

d. P(atleast 1)= 1-P(0)=1-(0.7)3=0.882351

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.