UNIT 5: PROBABILITYBasic Probability

Sample SpaceSet of all possible outcomes for a chance experiment.

Example: Rolling a Die

Probability Model

• It is a description of some chance process that consists of two parts• A sample space (S)• A probability for each outcome

Tree DiagramA technique for listing the outcomes in a sample space. It contains branches showing what can happen on different trials.

Draw diagram of all possibilities of test performance on three True/False questions.

Draw the tree diagram for winning the best 2 out of 3 games.

Imagine rolling two fair, six-sided dice – one that is red and one that is green. Give a probability model for this chance process.

Event• It is a subset of the sample space.

• It is usually designated by capital letters, like A, B, C, and so on.

Consider flipping 2 coins

A = both tails

B = at least one head

Find P(A) P(B)

Basic Rules of Probability – (don’t write yet)

Complement

Mutually Exclusive (Disjoint)

• Two events are mutually exclusive (disjoint) if they have no outcomes in common and so can never occur together.

Basic Probability Rules

Find the probability:• Rolling a 5

• Choosing a girl in this class

• Drawing a king

Two marbles are pulled from a bag holding one red, one white, one blue, and two green marbles.

A={the blue marble is drawn}

B={a green marble is drawn}

Distance learning courses are rapidly gaining popularity among college students. Randomly select an undergraduate student who is taking a distance-learning course for credit, and record the student’s age. Here is the probability model.

• Show that this is a legitimate probability model.

• Find the probability that the chosen student is not in the traditional college age group (18 to 23).

Age Group (Yr): 18 to 23 24 to 29 30 to 39 40 or over

Probability: 0.57 0.17 0.14 0.12

Choose an American adult at random. Define two events:A = the person has a cholesterol level of 240 mg per deciliter of blood (mg/dl) or above (high cholesterol).B = the person has a cholesterol level of 200 to 239 mg/dl (bordering high cholesterol)

According to the American Heart Association, P(A) = 0.16 and the P(B) = 0.29.

• Explain why events A and B are mutually exclusive.

• What is P(A and B)?

• What is P(A or B)?

• If C is the event that ther person chosen has normal cholesterol (below 200 mg/dl), what is P(C)?

Homework