Final answer:
The probability of selecting two defective AAA batteries from a box of 20 batteries with 3 defective units is approximately 1.58%.
Step-by-step explanation:
The probability of selecting two defective batteries from a box of 20 batteries, where 3 are defective, involves a hypergeometric distribution. The probabilities are determined by considering the number of ways to select defective batteries and the total number of ways to select any two batteries from the box.
To calculate the probability of selecting two defective batteries without replacement, we use the formula: P(X = k) = (K choose k) * ((N - K) choose (n - k)) / (N choose n), where 'K' is the total number of defective batteries, 'k' is the number of defective batteries chosen, 'N' is the total number of batteries, and 'n' is the number of batteries chosen. Substituting the given values, we have: P(two defective) = (3 choose 2) * (17 choose 0) / (20 choose 2).
Using the combinations formula, this calculates to:
P(two defective) = (3! / (2! * 1!)) * (17! / (17! * 0!)) / (20! / (2! * 18!)) = 3/190 or approximately 0.0158, which is 1.58%.