Note:A standard 52 card deck has half red cards and half black cards. The deck has fours suits: hearts, spades, clubs, and diamonds. Each suit has 13 different face cards.

Probabilities of simple events

  1. Suppose we draw a single card from a standard deck. What is the probability we draw a King?
  2. What is the probability we draw a red card?
  3. What is the probability we draw a card that is a heart?

The general addition rule

  1. Suppose we draw a single card from a standard deck. What is the probability that the card we draw is either a heart or an ace?
  2. In a hospital unit there are eight nurses and five physicians. Seven nurses and three physicians are females. If a staff person is selected, find the probability that the subject is a nurse or a male.
  3. At a political rally, there are 20 Republicans, 13 Democrats, and 5 Independents. If a person is selected, find the probability that he or she is either a Republican or an independent.
  4. Two dice are rolled. Find the probability of getting doubles or a sum of 4 or 6.

The multiplication rule for independent events

  1. Suppose we flip a coin 5 times. What is the probability we will get heads each time?
  2. Consider the following real statistic. 30% of bottled water samples are contaminated by such pollutants as arsenic and fecal bacteria. If two samples of bottled water are independently selected, what is the probability that both samples are contaminated by pollutants?

At the entrance to a casino, there are two slot machines. Machine A is programmed so that in the long run it will produce a winner in 10% of the plays. Machine B is programmed so that in the long run it will produce a winner in 15% of the plays.

  1. If we play each machine once, what is the probability that we will win on both plays?
  2. If we play each machine once, what is the probability that we will lose on both plays?
  3. If we play each machine once, what is the probability that we will win on at least one play?

Real data (as of 1999): Each day, 7% of the US population eat a meal at McDonald’s. If two people are randomly and independently selected, what is the probability that…

  1. …both people will eat a meal at McDonald’s today?
  2. …neither person will eat a meal at McDonald’s today?
  3. …at least one of them will eat a meal at McDonald’s today?