Answer:
The chance that there is one or more defective integrated circuits is 33.10%.
Detailed solution:
Each integrated circuit can be either defective or not, which provides only two possible outcomes. As a result, this scenario is well-suited to be analyzed using the binomial probability distribution.
About the binomial distribution
This distribution calculates the likelihood of exactly x successes in n repeated trials where each trial has two possible results.
Here, represents the count of combinations of x items selected from n elements, described by the formula:
And is the probability of the event X occurring.
Applying it to the problem
The product contains 40 integrated circuits, so .
The probability that an individual integrated circuit is defective is 0.01, so .
Finding the probability of at least one defective circuit
There are two cases: either at least one integrated circuit is defective (probability ) or none are defective (probability
). Since probabilities sum to 1, we want to determine
.
Hence, the probability of having one or more defective integrated circuits is 33.10%.