If the probability of a bulb malfunctioning is 0.2, what is the probability that at least 5 bulbs fail out of 6?

To determine the probability that at least 5 bulbs fail out of 6, we need to calculate the probabilities of exactly 5 bulbs malfunctioning and exactly 6 bulbs malfunctioning and then add these two probabilities together.

The term "at least 5" indicates that we are concerned with two scenarios: either 5 bulbs fail or all 6 bulbs fail. Thus, we denote these probabilities as P(5) for the case where 5 bulbs malfunction and P(6) for the case where all 6 bulbs malfunction. The combined probability of these two scenarios gives us the probability of having at least 5 failing bulbs.

The mathematical approach to find these probabilities involves using the binomial probability formula, which accounts for the number of trials (in this case, the number of bulbs), the probability of failure for each trial, and the number of successful outcomes desired (i.e., the malfunctioning bulbs).

By selecting the path that combines P(5) and P(6), you accurately cover all possible cases where "at least 5 bulbs fail." This is why the correct choice is the sum of these two probabilities, thus confirming the reasoning behind the choice.