unit 5: probability basic probability. sample space set of all possible outcomes for a chance...
TRANSCRIPT
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