EXAMPLE 1 Probability models

For the following three scenarios, determine whether or not a valid probability model exists:

  1. You ask your friend what his favorite ice cream flavor is.
    Outcome Probability
    Mint chocolate chip 0.25
    Pistachio −0.25
    Vanilla 0.50
    Other 0.50
  2. You ask another friend to go to a concert.
    Outcome Probability
    Yes 0.5
    No 0.5
    Maybe 0.5
  3. You play a single game of roulette and bet on red.
    Outcome Probability
    Win 0.47
    Lose 0.53

Solution

To be a valid probability model, each scenario must meet both rules of probability.

  1. The probability that your friend likes pistachio ice cream may not be very high, but it cannot be negative. This violates the first rule of probability that every event must have probability between zero and one. Note that, even though the second rule of probability is fulfilled (the probabilities sum to one), we nevertheless do not have a valid probability model here.
  2. Here, the first rule of probability is met, but the second one is violated. The sum of the three probabilities is . This is not equal to one, so that we do not have a valid probability model here either.
  3. Here, both probabilities lie between zero and one, so that the first rule of probability is met. Also, the sum of the two probabilities is , which fulfills the second rule of probability. Therefore, (c) represents a valid probability model.

NOW YOU CAN DO

Exercises 11–16.