A gumball machine has just been filled with 54 black 153 whi

A gumball machine has just been filled with 54 black, 153 white, 97 red and 95 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?

Solution

Probability of both/events occurring is found by multiplying the probabilities of the individual events.
Note that after Sue picks a red gumball, there are one less red and one less total gumballs for Jim.
The likelihood both Sue and Jim get red gumballs = (97/399)(96/398)

                                                                             = 9312/158802

                                                                             = 0.059