11.4 Fundamentals of Probability

Some important questions

What is probability?Why study probability?What is the probability of winning the Maryland

lottery?What is the probability of being struck by a

lightning?What is the probability of getting an A in the

class?

Computing Theoretical Probability

• If an event E has n(E) equally-likely outcomes and its sample space S has n(s) equally-likely outcomes, the theoretical probability of event E, denoted by P(E) is

P(E) = number of outcomes in event E = n(E)

total # of possible outcomes n(S)

Example 1

• A die is rolled once. Find the probability of getting:a. 5

b. an even number c. a number greater than 2 d. a number less than 6 e. a number greater than 4

Example 2

• You are dealt a standard 52-card deck. Find the probability of being dealt

• A. A king• B. A red card• C. A five• D. A picture card• E. A red queen• F. A club

Probabilities in Genetics

• Blood type problem: What is the chance of having a blood type AB if your parents have types AO and BB.

• Dimples: Facial dimples are examples of dominant genes which means that if a person has genotype DD or Dd, he or she will have a dimple. A person with no dimple has a genotype of dd. What is the chance of producing an offspring with a dimple if one parent has a dimple and the other has none?

Empirical Probability

• Theoretical probability is based on a set of equally-likely outcomes and the number of elements in a set. By contrast, empirical probability applies to situations in which we observe the frequency of occurrence of an event.

P (E) = observed number of times E occurs total number of observed occurences

Example• Marital Status of the US Population , Ages 18

or older in millions

Source: US Census Bureau

Never Married

Married Widowed Divorced Total

Male 28.6 62.1 2.7 9.0 102.4

Female 23.3 62.8 11.3 12.7 110.1

Total 51.9 124.9 14.0 21.7 212.5

Questions:

1. What is the probability of randomly selecting a female?

2. What is the probability of randomly selecting a divorced person?

3. What is the probability of randomly selecting a married male?

Assignments

• Classwork: Checkpoints 1-4 p. 580-584• And do #s 2-30 (evens)

• HW: p. 585-586, #s 1-39 (odd); 49-63 (odd)