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

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%