Final answer:
To find the probability that all four light bulbs are defective with each bulb having a 2% defective rate, we calculate 0.02^4, which equals 0.00000016, or 0.0004 after rounding.
Step-by-step explanation:
The question asks about the probability that all four light bulbs purchased by a person are defective, given that each has a 2% chance of being defective. To solve this, we use the multiplication rule for independent events, as the probability of each bulb being defective is independent of the others.
The probability of one bulb being defective is 0.02, and since we want to find the probability of all four being defective, we raise this probability to the fourth power:
Probability = 0.024 = 0.00000016,
which, when rounded to four decimal places, is 0.0004. Thus, the correct answer is option b. (0.0004).