The probability of rain tomorrow is 0.35. What is the probability that it does NOT rain?

The complement rule says $P(\text{not }A)=1-P(A)$. Here $1-0.35=0.65$, choice H. The probabilities of rain and no rain must add to $1$, and $0.35+0.65=1$. Choice F ($0.35$) is the probability of rain itself. Choice J ($1.35$) adds instead of subtracting, which gives an impossible probability greater than $1$. Choice G ($0.55$) comes from a subtraction slip. A probability is always between $0$ and $1$, so choice J can be eliminated without calculation.