Part 3 of 4 (c) What is the probability that fewer than 4 weigh more than 20 pounds? The probability that fewer than 4 weigh more than 20 pounds is \( \square \).

To answer this, we can use the binomial probability formula since we’re dealing with a scenario where there are specific outcomes (weigh more than 20 pounds or not) in a fixed number of trials. If we assume that the probability of any single object weighing more than 20 pounds is 'p', and the total number of objects is 'n', then we can determine the probability of fewer than 4 weighing more than 20 pounds by summing up the probabilities of the events where 0, 1, 2, or 3 objects exceed 20 pounds. For example, if the probability of an object weighing more than 20 pounds is 0.5, we would calculate: - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3), using the binomial formula: \[ P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} \] where \( \binom{n}{k} \) is the combination of n taken k at a time. Then, you simply add these probabilities together to find the total probability that fewer than 4 weigh more than 20 pounds. For instance, if you have 10 random items and you find out that there’s, say, a 30% chance per item. The complete math wizardry will unfold the probability neatly for you!