A researcher in a medical study screens prospective participants for having high serum cholesterol. Let represent the number of prospective participants screened until the fifth person wtih high serum cholesterol is found. It is known from past experience that the expected number of prospective participants screened until finding the fifth person with high serum cholesterol is 25. The researcher wants to know the likelihood of achieving his objective by screening just 12 to 15 prospective participants.
What is the probability of finding 5 participants with high serum cholesterol by screening 12 to 15 prospective participants (inclusive for both endpoints)?
One ball is drawn successively with replacement from an urn containing one red ball and three white balls. Find the probability that at most 6 draws are necessary to obtain 3 red balls.