Use the formula  C(n, x)pxqn − x to determine the probability of the given event. (Round your answer to four decimal places.) The probability of at least four successes in eight trials of a binomial experiment in which  p = 1/2

You purchase boxes of cereal until you obtain one with the collector's toy you want. If, on average, you get the toy you want in every 62th cereal box, what is the probability of getting the toy you want in any given cereal box? (Round your answer to 3 decimal places.)

Based on a survey, assume that 33% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when six consumers are randomly selected, exactly three of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting three consumers comfortable with drones followed by three consumers not comfortable, as in this calculation: (0.33)(0.33)(0.33)(0.67)(0.67)(0.67) = 0.0108? Choose the correct answer below. A. The event that a consumer is comfortable with drones is not mutually exclusive with the event that a consumer is not comfortable with drones. B. The probability of the second consumer being comfortable with drones cannot be treated as being independent of the probability of the first consumer being comfortable with drones. O C. There are other arrangements consisting of three consumers who are comfortable and three who are not. The probabilities corresponding to those other…

A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 3 insects will die? Round your answer to four decimal places.