A weather forecast gives a 30% chance of rain on each of the next two days, with the two days independent of each other. What is the…

Because the two days are independent, multiply the probabilities: $0.30\cdot0.30=0.09$, choice B. The chance of rain on both days must be less than the chance of rain on either day alone, and $0.09<0.30$. Choice D ($0.60$) adds the probabilities, which is not the rule for both events. Choice C ($0.30$) is the probability of rain on a single day. Choice A ($0.06$) is $0.3\cdot0.2$, using the wrong probability for the second day. Independence is what allows us to multiply.