A medical trial tests a new treatment. Out of 200 patients, 40% receive the treatment and 60% receive a placebo. Of those receiving the treatment, 75% show improvement. Of those receiving placebo, 20% show improvement.
(a) Complete a frequency tree showing actual frequencies.
(b) Calculate the probability that a randomly chosen patient shows improvement.
(c) Given a patient shows improvement, calculate the probability they were in the treatment group. Give your answer as a fraction in lowest terms.
(a)(a) Complete the frequency tree with actual numbers.(1)
(b)(b) Calculate the probability that a randomly chosen patient shows improvement.(2)
(c)(c) Given a patient shows improvement, calculate the probability they were in the treatment group. Give your answer as a fraction in lowest terms.(2)
(Total for Question 3 is 5 marks)