Addition Rule for Probability: for Any Events E and F from a Sample Space S, P (E U F)

Ch. 8.4 Basic Concepts of Probability

Addition Rule for Probability: For any events E and F from a sample space S, P (E U F) = P (E) + P (F) – P (E ∩ F)

Addition Rule for Disjoint Events:

P (E U F) = P (E) + P (F)

Ex1. In a group of 50 students, 23 take math, 11 take psychology, and 7 take both math and psychology. If one student is selected at random, find the probability that the student takes math or psychology.

Ex2. . In 2010, there were approximately 242 million Americans ages 15 or older. Table shows the distribution, by marital status and gender, of this population.

If one person randomly selected from the population described in table, find the probability, to the nearest hundredth, that the person

a) The person is divorced or male.

b) The person is married or divorced.

c) The person is married or female.

d) The person is divorced or widowed.

Ex3. Suppose two fair dice are rolled. Find each of the given probabilities.

a) The first die shows a 2 or the sum of the results is 6 or 7.

b) The sum is 11 or the second die shows a 5.

Ex4. Ex1. Roulette wheel that has 38numbered slots (1 through 66, 0, and 00). Of the 38 compartments, 18 are black, 18 are red, and 2 are green. A play has the dealer spin the wheel and a small ball in opposite directions. As the ball slows to a stop, it can land with equal probability on any one of the 38 numbered slots. Assume a single spin of the roulette wheel is made. Find the probability for the given events. The marble lands on an odd or black slot.

Ex5. Assume that the probability of a couple having a baby boy is the same as the probability of the couple having a baby girl. If the couple has 3 children, find the probability that at least 2 of them are girls.

Complement Rule: For any event E

P (E’) = 1 – P (E) and P (E) = 1 – P (E’)

Ex6. If you are dealt one card from a standard 52-card deck, find the probability that you are not dealt a queen.

Ex7.

a) If a fair die is rolled, what is the probability that any number but 5 will come up?

b) If two fair dice are rolled, find the probability that the sum of the numbers showing is greater than 3.

Ex8. You roll a single, six-sided die.

a) Find the odds in favor of rolling a 2.

b) Find the odds against rolling a 2.

Ex9. You are dealt one card from a 52-card deck.

a) Find the odds in favor of getting a red queen.

b) Find the odds against getting a red queen.

Ex10. The winner of a raffle will receive a new sports utility vehicle. If 500 raffle tickets were sold and you purchased ten tickers, what are the odds against your winning the car?

Ex11.The odds in favor of a particular house winning a race are 2 to 5. What is the probability that this horse will win the race?

Ex12. The odds against a particular horse winning a race are 15 to1. Find the odds in favor of the horse winning the race and the probability of the horse winning the race.