Presentation 1 Basic Concepts of Probability OBJECTIVES Identify

Presentation 1: Basic Concepts of Probability

OBJECTIVES ØIdentify the sample space of a probability experiment ØIdentify simple events

PROBABILITY EXPERIMENTS Probability experiment ØAn action, or trial, through which specific results (counts, measurements, or responses) are obtained. Outcome ØThe result of a single trial in a probability experiment. Sample Space ØThe set of all possible outcomes of a probability experiment. Event ØConsists of one or more outcomes and is a subset of the sample space.

PROBABILITY EXPERIMENTS ØProbability experiment: Roll a die ØOutcome: {3} ØSample space: {1, 2, 3, 4, 5, 6} ØEvent: {Die is even}={2, 4, 6}

EXAMPLE: IDENTIFYING THE SAMPLE SPACE A probability experiment consists of tossing a coin and then rolling a six-sided die. Describe the sample space.

EXAMPLE: IDENTIFYING THE SAMPLE SPACE A probability experiment consists of tossing a coin and then rolling a six-sided die. Describe the sample space. Solution: There are two possible outcomes when tossing a coin: a head (H) or a tail (T). For each of these, there are six possible outcomes when rolling a die: 1, 2, 3, 4, 5, or 6. One way to list outcomes for actions occurring in a sequence is to use a tree diagram.

SOLUTION: IDENTIFYING THE SAMPLE SPACE Tree diagram: H 1 H 2 H 3 H 4 H 5 H 6 T 1 T 2 T 3 T 4 T 5 T 6 The sample space has 12 outcomes: {H 1, H 2, H 3, H 4, H 5, H 6, T 1, T 2, T 3, T 4, T 5, T 6}

IDENTIFY THE SAMPLE SPACE ØGuessing the initial of a student’s middle name ØTossing 3 coins ØRolling a pair of 6 sided dice

Simple Events Simple Event ØAn event that consists of a single outcome. Øe. g. “Tossing heads and rolling a 3” {H 3} ØAn event that consists of more than one outcome is not a simple event. Øe. g. “Tossing heads and rolling an even number” {H 2, H 4, H 6}

Example: Identifying Simple Events Determine whether the event is simple or not. You roll a six-sided die. Event B is rolling at least a 4.

Example: Identifying Simple Events Determine whether the event is simple or not. You roll a six-sided die. Event B is rolling at least a 4. Solution: Not simple (event B has three outcomes: rolling a 4, a 5, or a 6)

SIMPLE OR NOT? ØA random number table is used to randomly select a number from 1 to 1000. Event A is selecting 932. ØYou randomly select one card from a deck of 52 playing cards. Event B is selecting an ace.