Course Notes - Department of Mathematics and Statistics

• A probability less than 0.05 is (by convention) taken to imply anevent is rare or unlikely to occur• A probability above 0.05 often means an event is not unusual.Cancer drug exampleThe standard drug for treating a cancer is claimed to halve thetumour size in 30% of all patients treated. Suppose X is the binomialrandom variable for the number of patients in a sample of seven whohave their tumour size halved.1. List the conditions which must be met if X is binomial2. Write down the probability that three of the patients have theirtumour size halved3. Find the probability that three or more of the patients have theirtumour size halved.4. In a pilot study in Auckland, three out of seven patients given anew drug had their tumour size halved. What conclusion if anycan be drawn about the new drug? Explain how you reach yourconclusionCancer drug example solutions1. List the conditions which must be met if X is binomial• Patients need to be independent, so we can’t select people fromthe same family or with any other common factor.• Two outcomes only - Cancer halved, or not halved.• Constant probability of tumour size halved over all the patients.- Can’t have some medical breakthrough in middle of trial.2. Write down the probability that three of the patients have theirtumour size halved = 0.2269.3. Find the probability that three or more of the patients have theirtumour size halved = 0.2269 + 0.0972 + 0.0250 + 0.0036 + 0.0002.67