Tree diagrams Tables Fundamental Counting Principle if one event has a possible outcomes and a second independent event has b possible outcomes, – then there are a b total possible outcomes for the two events together • Probability a ratio between the number of desired outcomes to the total possible outcomes, p≤1 – 0 ≤ Probability = Notation for probability P(event) The closer a probability of an outcome is to 1, the more likely the outcome will occur; whereas, the closer a probability of an outcome is to 0, the less likely the outcome will occur. Ex: Theoretical probability the likelihood of an event occurring without conducting an experiment – Experimental probability the likelihood of an event occurring from the outcomes of an experiment – Various types of experiments Ex: Coins, drawing objects out of box without looking, spinners with even and uneven sections, choosing a random card, marbles, number cubes, etc. Representation of probability as a fraction, decimal, or percent Ex: Three out of the ten sections are blue: , 0.3, 30% Complement of an event the probability of the non-occurrence of a desired outcome – Ex: The probability of selecting a face card from a deck of cards is or . The complement of selecting a face card from a deck of cards is the probability of selecting any card but a face card from a deck of cards which is or . The outcomes of an event and its complement complete the sample space. Relationship between an event and its complement expressed as a ratio or numerical expression The sum of the probability of an event and its complement will always be 1. Ex: If, P(A) = , then P(not A) = or . Therefore, P(A) + P(not A) = = 1 Relationship between theoretical and experimental probability Law of large numbers as the number of trials increases the difference between the experimental and theoretical probability will be closer to – zero Simple event an event that consists of a single outcome – Ex: Compound events events that consists of two or more simple events and consists of more than one outcome – Compound independent events events with more than one outcome, and one event does not affect the outcome of the other – Ex: Compound dependent events events with more than one outcome, and the outcome of one event affects the outcome of the subsequent – event or events
Tree diagrams Tables Fundamental Counting Principle – if one event has a possible outcomes and a second independent event has b possible outcomes, then there are a • b total possible outcomes for the two events together Probability – a ratio between the number of desired outcomes to the total possible outcomes, 0 ≤ p≤1 Probability = Notation for probability P(event) The closer a probability of an outcome is to 1, the more likely the outcome will occur; whereas, the closer a probability of an outcome is to 0, the less likely the outcome will occur. Ex: Theoretical probability – the likelihood of an event occurring without conducting an experiment Experimental probability – the likelihood of an event occurring from the outcomes of an experiment Various types of experiments Ex: Coins, drawing objects out of box without looking, spinners with even and uneven sections, choosing a random card, marbles, number cubes, etc. Representation of probability as a fraction, decimal, or percent Ex: Three out of the ten sections are blue: , 0.3, 30% Complement of an event – the probability of the non-occurrence of a desired outcome Ex: The probability of selecting a face card from a deck of cards is or . The complement of selecting a face card from a deck of cards is the probability of selecting any card but a face card from a deck of cards which is or . The outcomes of an event and its complement complete the sample space. Relationship between an event and its complement expressed as a ratio or numerical expression The sum of the probability of an event and its complement will always be 1. Ex: If, P(A) = , then P(not A) = or . Therefore, P(A) + P(not A) = = 1 Relationship between theoretical and experimental probability Law of large numbers – as the number of trials increases the difference between the experimental and theoretical probability will be closer to zero Simple event – an event that consists of a single outcome Ex: Compound events – events that consists of two or more simple events and consists of more than one outcome Compound independent events – events with more than one outcome, and one event does not affect the outcome of the other Ex: Compound dependent events – events with more than one outcome, and the outcome of one event affects the outcome of the subsequent event or events