A gumball machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. sue and jim, each, purchased one gumball. what is the likelihood both sue and jim get red gumballs

Exactly 33/532, or about 6.2% This is a conditional probability, So what we're looking for is the probability of 2 gumballs being selected both being red. So let's pick the first gumball. There is a total of 50+150+100+100 = 400 gumballs in the machine. Of them, 100 of the gumballs are red. So there's a 100/400 = 1/4 probability of the 1st gumball selected being red. Now there's only 399 gumballs in the machine and the probability of selecting another red one is 99/399 = 33/133. So the combined probability of both of the 1st 2 gumballs being red is 1/4 * 33/133 = 33/532, or about 0.062030075 = 6.2%