4 Eezimix flour is sold in small bags of weight \(S\) grams, where \(S \sim \mathrm {~N} \left( 502.1,0.31 ^ { 2 } \right)\). It is also sold in large bags of weight \(L\) grams, where \(L \sim \mathrm {~N} \left( 1004.9,0.58 ^ { 2 } \right)\).

1. Find the probability that a randomly chosen large bag weighs at least 1 gram more than two randomly chosen small bags.
2. Find the probability that a randomly chosen large bag weighs less than twice the weight of a randomly chosen small bag.