33/532 or approximately 6.2% that both Sue and Jim will get red gumballs.
For the purpose of this problem, going to group the gumballs into 2 sets. Red and anything else. The number of non-red gumballs is
50 + 150 + 100 = 300
The number of red gumballs is 100.
So what's the probability of 2 random picks both being a red gumball. For the 1st pick, it's a simple matter of 100/400 = 1/4.
For the second pick it's slightly more complicated since there's now only 99 red gumballs. So it's
99/399 = 33/133
To get the combined probability, just multiply them together.
33/133 * 1/4 = 33/532 which is approximately 6.2%
