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the objective is to calculate the probability of having at least one success and at least three failures in a burali trial with Nal 11 and P = 4/5 based on problem s from section 4.1 of the text one we are given a Burnal trial with n equal to 11 and P equal to 4/5 this means that the probability of success is 4/5 and the probability of failure is 1/5 two we want to find the probability of at least one success and at least three failures this means that we need to consider the cases where there are 1 to eight successes and thus three to 10 failures three we can use the binomial probability formula to calculate the probability for each case and then sum them up the binomial probability formula is PX equal to k equal to CN K asteris PK asteris minus PN minus kwx is the number of successes K is the number of successes we want to find the probability for n is the total number of Trials p is the probability of success and CN K is the number of combinations of n items taken k at a time four w
