Mathematics

The room needs at least two lamps working, so you're looking for the probability of "exactly two lamps OR all three lamps." Since the lamps are independent, calculate each scenario separately: find $P(\text{exactly 2 work})$ by considering which pair succeeds and which fails, then add $P(\text{all 3 work})$. The key is recognizing that these cases don't overlap, so you can simply add their probabilities.

The room needs at least two lamps working, so you're looking for the probability of "exactly two lamps OR all three lamps." Since the lamps are independent, calculate each scenario separately: find $P(\text{exactly 2 work})$ by considering which pair succeeds and which fails, then add $P(\text{all 3 work})$. The key is recognizing that these cases don't overlap, so you can simply add their probabilities.